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  • 1.
    Ahmad, M. Rauf
    et al.
    Linköpings universitet, Matematiska institutionen, Matematisk statistik. Linköpings universitet, Tekniska högskolan.
    Ohlson, Martin
    Linköpings universitet, Matematiska institutionen, Matematisk statistik. Linköpings universitet, Tekniska högskolan.
    von Rosen, Dietrich
    Linköpings universitet, Matematiska institutionen, Matematisk statistik. Linköpings universitet, Tekniska högskolan.
    A U-statistics Based Approach to Mean Testing for High Dimensional Multivariate Data Under Non-normality2011Rapport (Övrigt vetenskapligt)
    Abstract [en]

    A test statistic is considered for testing a hypothesis for the mean vector for multivariate data, when the dimension of the vector, p, may exceed the number of vectors, n, and the underlying distribution need not necessarily be normal. With n, p large, and under mild assumptions, the statistic is shown to asymptotically follow a normal distribution. A by product of the paper is the approximate distribution of a quadratic form, based on the reformulation of well-known Box's approximation, under high-dimensional set up.

  • 2.
    Ahmad, M. Rauf
    et al.
    Linköpings universitet, Matematiska institutionen, Matematisk statistik. Linköpings universitet, Tekniska högskolan.
    Ohlson, Martin
    Linköpings universitet, Matematiska institutionen, Matematisk statistik. Linköpings universitet, Tekniska högskolan.
    von Rosen, Dietrich
    Department of Energy and Technology, Swedish Univerity of Agricultural Sciences, SE-750 07 Uppsala, Sweden.
    Some Tests of Covariance Matrices for High Dimensional Multivariate Data2011Rapport (Övrigt vetenskapligt)
    Abstract [en]

    Test statistics for sphericity and identity of the covariance matrix are presented, when the data are multivariate normal and the dimension, p, can exceed the sample size, n. Using the asymptotic theory of U-statistics, the test statistics are shown to follow an approximate normal distribution for large p, also when p >> n. The statistics are derived under very general conditions, particularly avoiding any strict assumptions on the traces of the unknown covariance matrix. Neither any relationship between n and p is assumed. The accuracy of the statistics is shown through simulation results, particularly emphasizing the case when p can be much larger than n. The validity of the commonly used assumptions for high-dimensional set up is also briefly discussed.

  • 3.
    Ahmad, M. Rauf
    et al.
    Swedish University of Agricultural Sciences, Uppsala, Sweden and Department of Statistics, Uppsala University, Sweden.
    von Rosen, Dietrich
    Linköpings universitet, Matematiska institutionen, Matematisk statistik. Linköpings universitet, Tekniska högskolan.
    Singull, Martin
    Linköpings universitet, Matematiska institutionen, Matematisk statistik. Linköpings universitet, Tekniska högskolan.
    A note on mean testing for high dimensional multivariate data under non-normality2013Ingår i: Statistica neerlandica (Print), ISSN 0039-0402, E-ISSN 1467-9574, Vol. 67, nr 1, s. 81-99Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    A test statistic is considered for testing a hypothesis for the mean vector for multivariate data, when the dimension of the vector, p, may exceed the number of vectors, n, and the underlying distribution need not necessarily be normal. With n,p→∞, and under mild assumptions, but without assuming any relationship between n and p, the statistic is shown to asymptotically follow a chi-square distribution. A by product of the paper is the approximate distribution of a quadratic form, based on the reformulation of the well-known Box's approximation, under high-dimensional set up. Using a classical limit theorem, the approximation is further extended to an asymptotic normal limit under the same high dimensional set up. The simulation results, generated under different parameter settings, are used to show the accuracy of the approximation for moderate n and large p.

  • 4.
    Andrushchenko, Zhanna
    et al.
    Department of Biometry and Engineering SLU.
    Ohlson, Martin
    Linköpings universitet, Tekniska högskolan. Linköpings universitet, Matematiska institutionen, Matematisk statistik.
    von Rosen, Dietrich
    Department of Biometry and Engineering SLU.
    Estimation of banded covariance matrices in a multivariate normal distribution2008Rapport (Övrigt vetenskapligt)
  • 5.
    Berntsson, Fredrik
    et al.
    Linköpings universitet, Matematiska institutionen, Beräkningsmatematik. Linköpings universitet, Tekniska fakulteten.
    Ohlson, Martin
    Linköpings universitet, Matematiska institutionen, Matematisk statistik. Linköpings universitet, Tekniska fakulteten.
    More on Estimation of Banded and Banded Toeplitz Covariance Matrices2017Rapport (Övrigt vetenskapligt)
    Abstract [en]

    In this paper we consider two different linear covariance structures, e.g., banded and bended Toeplitz, and how to estimate them using different methods, e.g., by minimizing different norms.

    One way to estimate the parameters in a linear covariance structure is to use tapering, which has been shown to be the solution to a universal least squares problem. We know that tapering not always guarantee the positive definite constraints on the estimated covariance matrix and may not be a suitable method. We propose some new methods which preserves the positive definiteness and still give the correct structure.

    More specific we consider the problem of estimating parameters of a multivariate normal p–dimensional random vector for (i) a banded covariance structure reflecting m–dependence, and (ii) a banded Toeplitz covariance structure.

  • 6.
    Ekdahl, Magnus
    et al.
    Linköpings universitet, Matematiska institutionen, Matematisk statistik. Linköpings universitet, Tekniska högskolan.
    Koski, Timo
    Linköpings universitet, Matematiska institutionen, Matematisk statistik. Linköpings universitet, Tekniska högskolan.
    Ohlson, Martin
    Linköpings universitet, Matematiska institutionen, Matematisk statistik. Linköpings universitet, Tekniska högskolan.
    Concentrated or non-concentrated discrete distributions are almost independent2007Manuskript (preprint) (Övrigt vetenskapligt)
    Abstract [en]

    The task of approximating a simultaneous distribution with a product of distributions in a single variable is important in the theory and applications of classification and learning, probabilistic reasoning, and random algmithms. The evaluation of the goodness of this approximation by statistical independence amounts to bounding uniformly upwards the difference between a joint distribution and the product of the distributions (marginals). In this paper we develop a bound that uses information about the most probable state to find a sharp estimate, which is often as sharp as possible. We also examine the extreme cases of concentration and non-conccntmtion, respectively, of the approximated distribution.

  • 7.
    Evarest, Emanuel
    et al.
    Linköpings universitet, Matematiska institutionen, Matematisk statistik. Linköpings universitet, Tekniska fakulteten.
    Berntsson, Fredrik
    Linköpings universitet, Matematiska institutionen, Beräkningsmatematik. Linköpings universitet, Tekniska fakulteten.
    Singull, Martin
    Linköpings universitet, Matematiska institutionen, Matematisk statistik. Linköpings universitet, Tekniska fakulteten.
    Charles, Wilson
    Department of Mathematics, University of Dar es Salaam, Tanzania.
    Regime Switching models on Temperature Dynamics2016Rapport (Övrigt vetenskapligt)
    Abstract [en]

    Two regime switching models for predicting temperature dynamics are presented in this study for the purpose to be used for weather derivatives pricing. One is an existing model in the literature (Elias model) and the other is presented in this paper. The new model we propose in this study has a mean reverting heteroskedastic process in the base regime and a Brownian motion in the shifted regime. The parameter estimation of the two models is done by the use expectation-maximization (EM) method using historical temperature data. The performance of the two models on prediction of temperature dynamics is compared using historical daily average temperature data from five weather stations across Sweden. The comparison is based on the heating degree days (HDDs), cooling degree days (CDDs) and cumulative average temperature (CAT) indices. The expected HDDs, CDDs and CAT of the models are compared to the true indices from the real data. Results from the expected HDDs, CDDs and CAT together with their corresponding daily average plots demonstrate that, our model captures temperature dynamics relatively better than Elias model.

  • 8.
    Evarest, Emanuel
    et al.
    Linköpings universitet, Matematiska institutionen, Matematisk statistik. Linköpings universitet, Tekniska fakulteten.
    Berntsson, Fredrik
    Linköpings universitet, Matematiska institutionen, Beräkningsmatematik. Linköpings universitet, Tekniska fakulteten.
    Singull, Martin
    Linköpings universitet, Matematiska institutionen, Matematisk statistik. Linköpings universitet, Tekniska fakulteten.
    Charles, Wilson M.
    Department od Mathematics, University of Dar el Salaam, Tanzania.
    Regime Switching models on Temperature Dynamics2017Ingår i: International Journal of Applied Mathematics and Statistics, ISSN 0973-1377, E-ISSN 0973-7545, Vol. 56, nr 2Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    Two regime switching models for predicting temperature dynamics are presented in this study for the purpose to be used for weather derivatives pricing. One is an existing model in the literature (Elias model) and the other is presented in this paper. The new model we propose in this study has a mean reverting heteroskedastic process in the base regime and a Brownian motion in the shifted regime. The parameter estimation of the two models is done by the use expectation-maximization (EM) method using historical temperature data. The performance of the two models on prediction of temperature dynamics is compared using historical daily average temperature data from five weather stations across Sweden. The comparison is based on the heating degree days (HDDs), cooling degree days (CDDs) and cumulative average temperature (CAT) indices. The expected HDDs, CDDs and CAT of the models are compared to the true indices from the real data. Results from the expected HDDs, CDDs and CAT together with their corresponding daily average plots demonstrate that, our model captures temperature dynamics relatively better than Elias model.

  • 9.
    Evarest Sinkwembe, Emanuel
    et al.
    Linköpings universitet, Matematiska institutionen, Matematisk statistik. Linköpings universitet, Tekniska fakulteten.
    Berntsson, Fredrik
    Linköpings universitet, Matematiska institutionen, Beräkningsmatematik. Linköpings universitet, Tekniska fakulteten.
    Singull, Martin
    Linköpings universitet, Matematiska institutionen, Matematisk statistik. Linköpings universitet, Tekniska fakulteten.
    Yang, Xiangfeng
    Linköpings universitet, Matematiska institutionen, Matematisk statistik. Linköpings universitet, Tekniska fakulteten.
    Weather derivatives pricing using regim switching models2017Rapport (Övrigt vetenskapligt)
    Abstract [en]

    In this study we discuss the pricing of weather derivatives whose underlying weather variable is temperature. The dynamics of temperature in this study follows a two state regime switching model with a heteroskedastic mean reverting process as the base regime and a shifted regime defined by Brownian motion with mean different from zero. We develop the mathematical formulas for pricing futures contract on heating degree days (HDDs), cooling degree days (CDDs) and cumulative average temperature (CAT) indices. We also present the mathematical expressions for pricing the corresponding options on futures contracts for the same temperature indices. The local volatility nature of the model in the base regime captures very well the dynamics of the underlying process, thus leading to a better pricing processes for temperature derivatives contracts written on various index variables. We provide the description of Montecarlo simulation method for pricing weather derivatives under this model and use it to price a few weather derivatives call option contracts.

  • 10.
    Evarest Sinkwembe, Emanuel
    et al.
    Linköpings universitet, Matematiska institutionen, Matematisk statistik.
    Berntsson, Fredrik
    Linköpings universitet, Matematiska institutionen, Beräkningsmatematik. Linköpings universitet, Tekniska fakulteten.
    Singull, Martin
    Linköpings universitet, Matematiska institutionen, Matematisk statistik. Linköpings universitet, Tekniska fakulteten.
    Yang, Xiangfeng
    Linköpings universitet, Matematiska institutionen, Matematisk statistik. Linköpings universitet, Tekniska fakulteten.
    Weather Derivatives Pricing Using Regime Switching Model2018Ingår i: Monte Carlo Methods and Applications, ISSN 0929-9629, Vol. 24, nr 1, s. 13-27Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    In this study we discuss the pricing of weather derivatives whose underlying weather variable is temperature. The dynamics of temperature in this study follows a two state regime switching model with a heteroskedastic mean reverting process as the base regime and a shifted regime defined by Brownian motion with nonzero drift. We develop mathematical formulas for pricing futures and option contracts on heating degree days (HDDs), cooling degree days (CDDs) and cumulative average temperature (CAT) indices. The local volatility nature of the model in the base regime captures very well the dynamics of the underlying process, thus leading to a better pricing processes for temperature derivatives contracts written on various index variables. We use the Monte Carlo simulation method for pricing weather derivatives call option contracts.

  • 11.
    Habyarimana, Cassien
    et al.
    Integrated Polytechnic Regional Centre, Rwanda.
    Singull, Martin
    Linköpings universitet, Matematiska institutionen, Matematisk statistik. Linköpings universitet, Tekniska fakulteten.
    Nzabanita, Joseph
    University of Rwanda, Rwanda.
    Estimation of Parameters in the Growth Curve Model with a Linearly Structured Covariance Matrix: A Simulation Study2017Ingår i: International Journal of Scientific Engineering and Technology, ISSN 2277-1581, Vol. 6, nr 1, s. 45-49Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    In this paper, the implementation of algorithm proposed in (Nzabanita, J., et al. 2012) for some known linear structures on the covariance matrix Σ is performed and simulations for different sample sizes are repeated many times. For these simulations, the percentages of non positive definite estimates are produced, and the linear structures are identified and classified. 

  • 12.
    Herberthson, Magnus
    et al.
    Linköpings universitet, Matematiska institutionen, Matematik och tillämpad matematik. Linköpings universitet, Tekniska fakulteten.
    Johansson, KarinLinköpings universitet, Matematiska institutionen. Linköpings universitet, Tekniska fakulteten.Kozlov, VladimirLinköpings universitet, Matematiska institutionen, Matematik och tillämpad matematik. Linköpings universitet, Tekniska fakulteten.Ljungkvist, EmmaLinköpings universitet, Nationellt superdatorcentrum (NSC).Singull, MartinLinköpings universitet, Matematiska institutionen, Matematisk statistik. Linköpings universitet, Tekniska fakulteten.
    Proceedings from Workshop: Mathematics in Biology and Medicine, 11-12 May 2017, Linköping University2017Proceedings (redaktörskap) (Refereegranskat)
  • 13.
    John Mwakisisile, Andongwisye
    et al.
    Department of Mathematics, University of Dar es Salaam, Dar es Salaam, Tanzania.
    Larsson, Torbjörn
    Linköpings universitet, Matematiska institutionen, Optimeringslära. Linköpings universitet, Tekniska fakulteten.
    Ohlson, Martin
    Linköpings universitet, Matematiska institutionen, Matematisk statistik. Linköpings universitet, Tekniska fakulteten.
    Mushi, Allen
    Department of Mathematics, University of Dar es Salaam, Dar es Salaam, Tanzania.
    Asset liability management for Tanzania pension funds by stochastic programming2018Ingår i: Afrika Statistika, ISSN 2316-090XArtikel i tidskrift (Refereegranskat)
  • 14.
    John Mwakisisile, Andongwisye
    et al.
    Department of Mathematics, University of Dar es Salaam, Dar es Salaam, Tanzania.
    Larsson, Torbjörn
    Linköpings universitet, Matematiska institutionen, Optimeringslära. Linköpings universitet, Tekniska fakulteten.
    Singull, Martin
    Linköpings universitet, Matematiska institutionen, Matematisk statistik. Linköpings universitet, Tekniska fakulteten.
    Mushi, Allen
    Department of Mathematics, University of Dar es Salaam, Dar es Salaam, Tanzania.
    Projecting Tanzania Pension Fund System2017Ingår i: African Journal of Applied Statistics, ISSN 2316-0861, Vol. 4, nr 1, s. 193-218Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    A mandatory Tanzania pension fund with a final salary defined benefit is analyzed. This fund is a contributory pay-as-you-go defined benefit pension system which is much affected by the change in demography. Two kinds of pension benefit, a commuted (at retirement) and a monthly (old age) pension are considered. A decisive factor in the analysis is the increased life expectancy of members of the fund. The projection of the fund’s future members and retirees is done using expected mortality rates of working population and expected longevity. The future contributions, benefits, asset values and liabilities are analyzed. The projection shows that the fund will not be fully sustainable on a long term due to the increase in life expectancy of its members. The contributions will not cover the benefit payouts and the asset value will not fully cover liabilities. Evaluation of some possible reforms of the fund shows that they cannot guarantee a long-term sustainability. Higher returns on asset value will improve the funding ratio, but contributions are still insufficient to cover benefit payouts.

  • 15.
    Karlsson, Emil
    et al.
    Linköpings universitet, Matematiska institutionen, Optimeringslära. Linköpings universitet, Tekniska fakulteten.
    Singull, Martin
    Linköpings universitet, Matematiska institutionen, Matematisk statistik. Linköpings universitet, Tekniska fakulteten.
    More on explicit estimators for a banded covariance matrix2015Ingår i: Acta et Commentationes Universitatis Tartuensis de Mathematica, ISSN 1406-2283, E-ISSN 2228-4699, Vol. 19, nr 1, s. 49-62Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    The problem of estimating mean and covariances of a multivariate normally distributed random vector has been studied in many forms. This paper focuses on the estimators proposed by Ohlson et al. (2011) for a banded covariance structure with m-dependence. We rewrite the estimator when m = 1, which makes it easier to analyze. This leads to an adjustment, and an unbiased estimator can be proposed. A new and easier proof of consistency is then presented.

    This theory is also generalized to a general linear model where the corresponding theorems and propositions are stated to establish unbiasedness and consistency.

  • 16.
    Kozlov, Vladimir
    et al.
    Linköpings universitet, Matematiska institutionen, Tillämpad matematik. Linköpings universitet, Tekniska högskolan.
    Ohlson, MartinLinköpings universitet, Matematiska institutionen, Matematisk statistik. Linköpings universitet, Tekniska högskolan.von Rosen, DietrichLinköpings universitet, Matematiska institutionen, Matematisk statistik. Linköpings universitet, Tekniska högskolan.
    Proceedings of Workshops on Inverse Problems, Data, Mathematical Statistics and Ecology2011Proceedings (redaktörskap) (Övrigt vetenskapligt)
    Abstract [en]

    Processes in Nature may be considered as deterministic or/and random. We are observing global problems such as climate changes (e.g. warming and extreme weather conditions), pollutions (e.g. acidification, fertilization, the spread of many types of pollutants through air and water) and whole ecosystems that are under pressure (e.g. the Baltic sea and the Arctic region). To understand the processes in Nature and (predict) understand what might occur it is not enough with empirical studies. One needs theoretical fundaments including models and theories to perform correct actions against different threats or at least to carry out appropriate simulation studies. For example, extreme value theory can explain some of the observed phenomena, classical risk analysis may be of help, different types of multivariate and high-dimensional analysis can explain data, time series analysis is essential, for forthcoming studies the theory of experimental designs is of interest, data assimilation together with inverse problem technique is useful for adjustment of data into mathematical models and the list can be made much longer. Behind all these approaches mathematics is hidden, sometimes at a very advanced level. Chemical and physical processes influence all observations but the challenge is to do appropriate approximations so that mathematical/statistical models can be applied. The main aim of this project is to present state of the art knowledge concerning the modelling of Nature with focus on mathematical modelling, in particular "inverse and ill-posed problems", as well as spatiotemporal models. Inverse and ill-posed problems are characterized by the property that the solutions are extremely sensitive to measurement and modelling errors. There are established connections between inverse problems and Bayesian inference but very little has been carried out with focus on parametric inference such as the likelihood approach. Concerning spatio-temporal models these are usually extensions of classical time series models or/and classical multivariate analysis models.

    From the Nordic Council of Ministers, within the program Nordic - Russian Cooperation in Education and Research we asked for funding of 3 preparatory meetings where the plan was to create a series of events taking place during 2011-2013. Partner organizations were

    • Institute of Problems of Mechanical Engineering, St. Petersburg
    • St. Petersburg State University
    • Helsinki University
    • Swedish Agricultural University
    • Stockholm University
    • Linköping University

    However, there were also some other participants from other universities.

    The planned events should be connected to the following fields: applied mathematics, biophysics and mathematical statistics. Within applied mathematics: mathematical modelling and partial differential equations, inverse and ill-pose problems, data assimilation, dynamical systems, linear algebra, matrix theory; within biophysics; neural networks and inverse modelling of objects; within mathematical statistical; analyses of stochastic processes, spatio-temporal modelling, experimental design, where considered. There exists a wide overlap between these areas and it is challenging to systemize this overlap and transmit this knowledge to students and stakeholders. However, due to unsure funding it was decided to discuss what can be presented during a one-year program. Moreover, due to practical reasons only 2 meetings/workshops were held:

    1. Workshop on Inverse Problems, Data, Mathematical Statistics and Ecology: May 20-21, 2010 at Department of Mathematics, Linköping University.
    2. Workshop on Inverse Problems, Data, Mathematical Statistics and Ecology, Part II: August 25-27, 2010 at Department of Mathematics, Helsinki University.

    The output from the above events can be summarized as follows:

    • We have identified a number of different areas which can be taught on from different perspectives depending on students background of mathematics.
    • We have learned to know many interesting researchers who are willing to share there experiences when for example creating a summer school.
    • There is no doubt that we can organize cross-disciplinary summer/winter schools with focus on either the Baltic or Archtic regions.

    This booklet is also part of the deliverables. It comprizes extended abstracts of the majority of the talks of the participants showing their great interest. It is in some way a unique cross-disciplinary document which has joined researchers from different areas from Russia, Finland and Sweden.

    We are extremely grateful for the support given by the Nordic Council of Ministers (NCM-RU-PA-2009/10382) and all the enthusiastic contributions by the participants, including our host in Helsinki, professor Lassi Päivärinta.

    Vladimir Kozlo, Linköping University

    Martin Ohlso, Linköping University

    Dietrich von Rosen, Linköping University/SLU

  • 17.
    Ngaruye, Innocent
    et al.
    Linköpings universitet, Matematiska institutionen, Matematisk statistik. Linköpings universitet, Tekniska högskolan. Department of Mathematics, College of Science and Technology, University of Rwanda, P.O. Box 3900 Kigali, Rwanda.
    Nzabanita, Joseph
    Linköpings universitet, Matematiska institutionen, Matematisk statistik. Linköpings universitet, Tekniska högskolan. Department of Mathematics, College of Science and Technology, University of Rwanda, P.O. Box 3900 Kigali, Rwanda.
    von Rosen, Dietrich
    Linköpings universitet, Matematiska institutionen, Matematisk statistik. Linköpings universitet, Tekniska högskolan. Department of Energy and Technology, Swedish University of Agricultural Sciences, SE- 750 07 Uppsala, Sweden.
    Singull, Martin
    Linköpings universitet, Matematiska institutionen, Matematisk statistik. Linköpings universitet, Tekniska högskolan.
    Small Area Estimation under a Multivariate Linear Model for Repeated Measures Data2015Rapport (Övrigt vetenskapligt)
    Abstract [en]

    In this paper, we consider small area estimation under a multivariate linear regression model for repeated measures data. The aim of the proposed model is to get a model which borrows strength across small areas and over time, by incorporating simultaneously the area effects and time correlation. The model accounts for repeated surveys, group individuals and random effects variations. Estimation of model parameters is discussed within a restricted maximum likelihood based approach. Prediction of random e ects and the prediction of small area means across time points and per group units for all time points are derived. The results are supported by a simulation study.

  • 18.
    Ngaruye, Innocent
    et al.
    Linköpings universitet, Matematiska institutionen, Matematisk statistik. Linköpings universitet, Tekniska fakulteten.
    Nzabanita, Joseph
    Department of Mathematics, University of Rwanda.
    von Rosen, Dietrich
    Linköpings universitet, Matematiska institutionen, Matematisk statistik. Linköpings universitet, Tekniska fakulteten.
    Singull, Martin
    Linköpings universitet, Matematiska institutionen, Matematisk statistik. Linköpings universitet, Tekniska fakulteten.
    Small Area Estimation under a Multivariate Linear Model for Repeated measures Data2017Ingår i: Communications in Statistics - Theory and Methods, ISSN 0361-0926, E-ISSN 1532-415X, Vol. 46, nr 21, s. 10835-10850Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    In this article, Small Area Estimation under a Multivariate Linear model for repeated measures data is considered. The proposed model aims to get a model which borrows strength both across small areas and over time. The model accounts for repeated surveys, grouped response units and random effects variations. Estimation of model parameters is discussed within a likelihood based approach. Prediction of random effects, small area means across time points and per group units are derived. A parametric bootstrap method is proposed for estimating the mean squared error of the predicted small area means. Results are supported by a simulation study.

  • 19.
    Ngaruye, Innocent
    et al.
    Department of Mathematics, University of Rwanda.
    von Rosen, Dietrich
    Linköpings universitet, Matematiska institutionen, Matematisk statistik. Linköpings universitet, Tekniska fakulteten.
    Ohlson, Martin
    Linköpings universitet, Matematiska institutionen, Matematisk statistik. Linköpings universitet, Tekniska fakulteten.
    Small area estimation with missing data using a multivariate linear random effects model2018Ingår i: Japanese Journal of Statistics and Data Science, ISSN 2520-8756Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    In this article small area estimation with multivariate data that follow a monotonic missing sample pattern is addressed. Random effects growth curve models with covariates are formulated. A likelihood based approach is proposed for estimation of the unknown parameters. Moreover, the prediction of random effects and predicted small area means are also discussed.

  • 20.
    Ngaruye, Innocent
    et al.
    Linköpings universitet, Matematiska institutionen, Matematisk statistik. Linköpings universitet, Tekniska fakulteten.
    von Rosen, Dietrich
    Linköpings universitet, Matematiska institutionen, Matematisk statistik. Linköpings universitet, Tekniska fakulteten.
    Singull, Martin
    Linköpings universitet, Matematiska institutionen, Matematisk statistik. Linköpings universitet, Tekniska fakulteten.
    Crop yield estimation at district level for agricultural seasons 2014 in Rwanda2016Ingår i: African Journal of Applied Statistics, ISSN 2316-0861, Vol. 3, nr 1, s. 69-90Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    In this paper, we discuss an application of Small Area Estimation (SAE) tech- niques under a multivariate linear regression model for repeated measures data to produce district level estimates of crop yield for beans which comprise two varieties, bush beans and climbing beans in Rwanda during agricultural seasons 2014. By using the micro data of National Institute of Statistics of Rwanda (NISR) obtained from the Seasonal Agricul- tural Survey (SAS) 2014 we derive efficient estimates which show considerable gain. The considered model and its estimates may be useful for policy-makers or for further analyses. 

  • 21.
    Ngaruye, Innocent
    et al.
    Linköpings universitet, Matematiska institutionen, Matematisk statistik. Linköpings universitet, Tekniska fakulteten. Department of Mathematics, College of Science and Technology, University of Rwanda, Kigali, Rwanda.
    von Rosen, Dietrich
    Linköpings universitet, Matematiska institutionen, Matematisk statistik. Linköpings universitet, Tekniska fakulteten. Department of Energy and Technology, Swedish University of Agricultural Sciences, Uppsala, Sweden.
    Singull, Martin
    Linköpings universitet, Matematiska institutionen, Matematisk statistik. Linköpings universitet, Tekniska fakulteten. Department of Energy and Technology, Swedish University of Agricultural Sciences, Uppsala, Sweden.
    Mean-squared errors of small area estimators under a multivariate linear model for repeated measures data2017Rapport (Övrigt vetenskapligt)
    Abstract [en]

    In this paper, we discuss the derivation of the first and second moments for the proposed small area estimators under a multivariate linear model for repeated measures data. The aim is to use these moments to estimate the mean-squared errors (MSE) for the predicted small area means as a measure of precision. A two stage estimator of MSE is obtained. At the first stage, we derive the MSE when the covariance matrices are known. To obtain an unbiased estimator of the MSE, at the second stage, a method based on parametric bootstrap is  proposed for bias correction and for prediction error that reects the uncertainty when the unknown covariance is replaced by its suitable estimator.

  • 22.
    Ngaruye, Innocent
    et al.
    Linköpings universitet, Matematiska institutionen, Matematisk statistik. Linköpings universitet, Tekniska fakulteten. University of Rwanda.
    von Rosen, Dietrich
    Linköpings universitet, Matematiska institutionen, Matematisk statistik. Linköpings universitet, Tekniska fakulteten.
    Singull, Martin
    Linköpings universitet, Matematiska institutionen, Matematisk statistik. Linköpings universitet, Tekniska fakulteten.
    Mean-Squared errors of small area estimators under a multivariate linear model for repeated measures data2018Ingår i: Communications in Statistics - Theory and Methods, ISSN 0361-0926, E-ISSN 1532-415X, s. 1-23Artikel i tidskrift (Refereegranskat)
  • 23.
    Ngaruye, Innocent
    et al.
    Linköpings universitet, Matematiska institutionen, Matematisk statistik. Linköpings universitet, Tekniska fakulteten. Swedish Univ Agr Sci, Sweden.
    von Rosen, Dietrich
    Linköpings universitet, Matematiska institutionen, Matematisk statistik. Linköpings universitet, Tekniska fakulteten. Univ Rwanda, Rwanda.
    Singull, Martin
    Linköpings universitet, Matematiska institutionen, Matematisk statistik. Linköpings universitet, Tekniska fakulteten.
    Mean-Squared errors of small area estimators under a multivariate linear model for repeated measures data2019Ingår i: Communications in Statistics - Theory and Methods, ISSN 0361-0926, E-ISSN 1532-415X, Vol. 48, nr 8, s. 2060-2073Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    In this paper, we discuss the derivation of the first and second moments for the proposed small area estimators under a multivariate linear model for repeated measures data. The aim is to use these moments to estimate the mean-squared errors (MSE) for the predicted small area means as a measure of precision. At the first stage, we derive the MSE when the covariance matrices are known. At the second stage, a method based on parametric bootstrap is proposed for bias correction and for prediction error that reflects the uncertainty when the unknown covariance is replaced by its suitable estimator.

  • 24.
    Ngaruye, Innocent
    et al.
    Linköpings universitet, Matematiska institutionen, Matematisk statistik. Linköpings universitet, Tekniska fakulteten. Department of Mathematics, College of Science and Technology, University of Rwanda, Kigali, Rwanda.
    von Rosen, Dietrich
    Linköpings universitet, Matematiska institutionen, Matematisk statistik. Linköpings universitet, Tekniska fakulteten. Department of Energy and Technology, Swedish University of Agricultural Sciences, Uppsala, Sweden.
    Singull, Martin
    Linköpings universitet, Matematiska institutionen, Matematisk statistik. Linköpings universitet, Tekniska fakulteten.
    Small area estimation under a multivariate linear model for incomplete repeated measures data2017Rapport (Övrigt vetenskapligt)
    Abstract [en]

    In this paper, the issue of analysis of multivariate repeated measures data that follow a monotonic sample pattern for small area estimation is addressed. Random effects growth curve models with covariates for both complete and incomplete data are formulated. A conditional likelihood based approach is proposed for estimation of the mean parameters and covariances. Further, the prediction of random effects and predicted small area means are also discussed. The proposed techniques may be useful for small area estimation under longitudinal surveys with grouped response units and drop outs.

  • 25.
    Ngaruye, Innocent
    et al.
    Linköpings universitet, Matematiska institutionen, Matematisk statistik. Linköpings universitet, Tekniska fakulteten. Department of Mathematics, College of Science and Technology, University of Rwanda.
    von Rosen, Dietrich
    Linköpings universitet, Matematiska institutionen, Matematisk statistik. Linköpings universitet, Tekniska fakulteten. Department of Energy and Technology, Swedish University of Agricultural Sciences.
    Singull, Martin
    Linköpings universitet, Matematiska institutionen, Matematisk statistik. Linköpings universitet, Tekniska fakulteten.
    Small area estimation with missing data using a multivariate linear random effects model2017Rapport (Övrigt vetenskapligt)
    Abstract [en]

    In this article small area estimation with multivariate data that follow a monotonic missing sample pattern is addressed. Random effects growth curve models with covariates are formulated. A likelihood based approach is proposed for estimation of the unknown  parameters. Moreover, the prediction of random effects and predicted small area means are also discussed.

  • 26.
    Nzabanita, Joseph
    et al.
    Linköpings universitet, Matematiska institutionen, Matematisk statistik. Linköpings universitet, Tekniska högskolan.
    Singull, Martin
    Linköpings universitet, Matematiska institutionen, Matematisk statistik. Linköpings universitet, Tekniska högskolan.
    von Rosen, Dietrich
    Swedish University of Agricultural Sciences.
    Estimation of parameters in the extended growth curve model with a linearly structured covariance matrix2012Ingår i: Acta et Commentationes Universitatis Tartuensis de Mathematica, ISSN 1406-2283, E-ISSN 2228-4699, Vol. 16, nr 1, s. 13-32Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    In this paper the extended growth curve model with two terms and a linearly structured covariance matrix is considered. We propose an estimation procedure that handles linear structured covariance matrices. The idea is first to estimate the covariance matrix when it should be used to define an inner product in a regression space and thereafter reestimate it when it should be interpreted as a dispersion matrix. This idea is exploited by decomposing the residual space, the orthogonal complement to the design space, into three orthogonal subspaces. Studying residuals obtained from projections of observations on these subspaces yields explicit consistent estimators of the covariance matrix. An explicit consistent estimator of the mean is also proposed and numerical examples are given.

  • 27.
    Nzabanita, Joseph
    et al.
    Linköpings universitet, Matematiska institutionen, Matematisk statistik. Linköpings universitet, Tekniska fakulteten.
    von Rosen, Dietrich
    Linköpings universitet, Matematiska institutionen, Matematisk statistik. Linköpings universitet, Tekniska fakulteten. Department of Mathematics, University of Rwanda, Rwanda.
    Singull, Martin
    Linköpings universitet, Matematiska institutionen, Matematisk statistik. Linköpings universitet, Tekniska fakulteten.
    Bilinear regression model with Kronecker and linear structures for the covariance matrix2015Ingår i: Afrika Statistika, ISSN 2316-090X, Vol. 10, nr 2, s. 827-837Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    In this paper, the bilinear regression model based on normally distributed random matrix is studied. For these models, the dispersion matrix has the so called Kronecker product structure and they can be used for example to model data with spatio-temporal relationships. The aim is to estimate the parameters of the model when, in addition, one covariance matrix is assumed to be linearly structured. On the basis of n independent observations from a matrix normal distribution, estimating equations in a flip-flop relation are established and the consistency of estimators is studied.

  • 28.
    Nzabanita, Joseph
    et al.
    Linköpings universitet, Matematiska institutionen, Matematisk statistik. Linköpings universitet, Tekniska högskolan.
    von Rosen, Dietrich
    Swedish University of Agricultural Sciences.
    Singull, Martin
    Linköpings universitet, Matematiska institutionen, Matematisk statistik. Linköpings universitet, Tekniska högskolan.
    Estimation in multivariate linear models with Kronecker product and linear structures on the covariance matricesManuskript (preprint) (Övrigt vetenskapligt)
    Abstract [en]

    This paper deals with models based on normally distributed random matrices. More specifically the model considered is X ∼ Np,q(M, Σ, Ψ) with mean M, a p×q matrix, assumed to follow a bilinear structure, i.e., E[X] = M = ABC, where A and C are known design matrices, B is unkown parameter matrix, and the dispersion matrix of X has a Kronecker product structure, i.e., D[X] = Ψ ⊗ Σ, where both Ψ and Σ are unknown positive definite matrices. The model may be used for example to model data with spatiotemporal relationships. The aim is to estimate the parameters of the model when, in addition, Σ is assumed to be linearly structured. In the paper, on the basis of n independent observations on the random matrix X, estimation equations in a flip-flop relation are presented and numerical examples are given.

  • 29.
    Nzabanita, Joseph
    et al.
    Linköpings universitet, Matematiska institutionen, Matematisk statistik. Linköpings universitet, Tekniska högskolan. University of Rwanda, PO.Box 3900 Kigali, Rwanda.
    von Rosen, Dietrich
    Linköpings universitet, Matematiska institutionen, Matematisk statistik. Linköpings universitet, Tekniska högskolan. Department of Energy and Technology, Swedish University of Agricultural Sciences, SE–750 07 Uppsala, Sweden..
    Singull, Martin
    Linköpings universitet, Matematiska institutionen, Matematisk statistik. Linköpings universitet, Tekniska högskolan.
    Extended GMANOVA Model with a Linearly Structured Covariance Matrix2015Rapport (Övrigt vetenskapligt)
    Abstract [en]

    In this paper we consider the extended generalized multivariate analysis of variance (GMANOVA) with a linearly structured covariance matrix. The main theme is to find explicit estimators for the mean and for the linearly structured covariance matrix. We show how to decompose the residual space, the orthogonal complement to the mean space, into m + 1 orthogonal subspaces and how to derive explicit estimators of the covariance matrix from the sum of squared residuals obtained by projecting observations on those subspaces. Also an explicit estimator of the mean is derived and some properties of the proposed estimators are studied.

  • 30.
    Nzabanita, Joseph
    et al.
    Linköpings universitet, Matematiska institutionen, Matematisk statistik. Linköpings universitet, Tekniska fakulteten. University of Rwanda, Department of Mathematics.
    von Rosen, Dietrich
    Linköpings universitet, Matematiska institutionen, Matematisk statistik. Linköpings universitet, Tekniska fakulteten. Department of Energy and Technology Swedish University of Agricultural Sciences Uppsala, Sweden..
    Singull, Martin
    Linköpings universitet, Matematiska institutionen, Matematisk statistik. Linköpings universitet, Tekniska fakulteten.
    Extended GMANOVA Model with a Linearly Structured Covariance Matrix2015Ingår i: Mathematical Methods of Statistics, ISSN 1066-5307, E-ISSN 1934-8045, Vol. 24, nr 4, s. 280-291Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    In this paper we consider the extended generalized multivariate analysis of variance (GMANOVA) with a linearly structured covariance matrix. The main theme is to find explicit estimators for the mean and for the linearly structured covariance matrix. We show how to decompose the residual space, the orthogonal complement to the mean space, into m + 1 orthogonal subspaces and how to derive explicit estimators of the covariance matrix from the sum of squared residuals obtained by projecting observations on those subspaces. Also an explicit estimator of the mean is derived and some properties of the proposed estimators are studied. 

  • 31.
    Nzabanita, Joseph
    et al.
    Linköpings universitet, Matematiska institutionen, Matematisk statistik. Linköpings universitet, Tekniska högskolan. University of Rwanda, PO.Box 3900 Kigali, Rwanda.
    von Rosen, Dietrich
    Linköpings universitet, Matematiska institutionen, Matematisk statistik. Linköpings universitet, Tekniska högskolan. bDepartment of Energy and Technology, Swedish University of Agricultural Sciences, SE–750 07 Uppsala, Sweden..
    Singull, Martin
    Linköpings universitet, Matematiska institutionen, Matematisk statistik. Linköpings universitet, Tekniska högskolan.
    Maximum Likelihood Estimation in the Tensor Normal Model with a Structured Mean2015Rapport (Övrigt vetenskapligt)
    Abstract [en]

    There is a growing interest in the analysis of multi-way data. In some studies the inference about the dependencies in three-way data is done using the third order tensor normal model, where the focus is on the estimation of the variance-covariance matrix which has a Kronecker product structure. Little attention is paid to the structure of the mean, though, there is a potential to improve the analysis by assuming a structured mean. In this paper, we introduce a 2-fold growth curve model by assuming a trilinear structure for the mean in the tensor normal model and propose an algorithm for estimating parameters. Also, some direct generalizations are presented.

  • 32.
    Ohlson, Martin
    Linköpings universitet, Matematiska institutionen, Matematisk statistik. Linköpings universitet, Tekniska högskolan.
    Distribution of Quadratic Forms2007Konferensbidrag (Övrigt vetenskapligt)
    Abstract [en]

    A well known fact is that when testing hypotheses for covariance matrices, distributions of quadratic forms arise. A generalization of the distribution of the multivariate quadratic form XAX', where X is a p times n normally distributed matrix and A is a n times n symmetric real matrix, is presented. It is shown that the distribution of the quadratic form is the same as the distribution of a weighted sum of noncentral Wishart distributed matrices.

    Using this characterization of the distribution several properties of the quadratic form XAX' will be shown.

  • 33.
    Ohlson, Martin
    Linköpings universitet, Tekniska högskolan. Linköpings universitet, Matematiska institutionen, Matematisk statistik.
    Explicit estimators under m-dependence for a multivariate normal distribution2008Ingår i: LINSTAT2008,2008, 2008, s. 108-108Konferensbidrag (Övrigt vetenskapligt)
    Abstract [en]

        

  • 34.
    Ohlson, Martin
    Linköpings universitet, Matematiska institutionen, Matematisk statistik. Linköpings universitet, Tekniska högskolan.
    More on Distributions of Quadratic Forms2007Konferensbidrag (Övrigt vetenskapligt)
  • 35.
    Ohlson, Martin
    Linköpings universitet, Matematiska institutionen, Matematisk statistik. Linköpings universitet, Tekniska högskolan.
    Studies in Estimation of Patterned Covariance Matrices2009Doktorsavhandling, sammanläggning (Övrigt vetenskapligt)
    Abstract [en]

    Many testing, estimation and confidence interval procedures discussed in the multivariate statistical literature are based on the assumption that the observation vectors are independent and normally distributed. The main reason for this is that often sets of multivariate observations are, at least approximately, normally distributed. Normally distributed data can be modeled entirely in terms of their means and variances/covariances. Estimating the mean and the covariance matrix is therefore a problem of great interest in statistics and it is of great significance to consider the correct statistical model. The estimator for the covariance matrix is important since inference on the mean parameters strongly depends on the estimated covariance matrix and the dispersion matrix for the estimator of the mean is a function of it.

    In this thesis the problem of estimating parameters for a matrix normal distribution with different patterned covariance matrices, i.e., different statistical models, is studied.

    A p-dimensional random vector is considered for a banded covariance structure reflecting m-dependence. A simple non-iterative estimation procedure is suggested which gives an explicit, unbiased and consistent estimator of the mean and an explicit and consistent estimator of the covariance matrix for arbitrary p and m.

    Estimation of parameters in the classical Growth Curve model when the covariance matrix has some specific linear structure is considered. In our examples maximum likelihood estimators can not be obtained explicitly and must rely on numerical optimization algorithms. Therefore explicit estimators are obtained as alternatives to the maximum likelihood estimators. From a discussion about residuals, a simple non-iterative estimation procedure is suggested which gives explicit and consistent estimators of both the mean and the linearly structured covariance matrix.

    This thesis also deals with the problem of estimating the Kronecker product structure. The sample observation matrix is assumed to follow a matrix normal distribution with a separable covariance matrix, in other words it can be written as a Kronecker product of two positive definite matrices. The proposed estimators are used to derive a likelihood ratio test for spatial independence. Two cases are considered, when the temporal covariance is known and when it is unknown. When the temporal covariance is known, the maximum likelihood estimates are computed and the asymptotic null distribution is given. In the case when the temporal covariance is unknown the maximum likelihood estimates of the parameters are found by an iterative alternating algorithm and the null distribution for the likelihood ratio statistic is discussed.

    Delarbeten
    1. On the Distribution of Matrix Quadratic Forms
    Öppna denna publikation i ny flik eller fönster >>On the Distribution of Matrix Quadratic Forms
    2012 (Engelska)Ingår i: Communications in Statistics - Theory and Methods, ISSN 0361-0926, E-ISSN 1532-415X, Vol. 41, nr 18, s. 3403-315Artikel i tidskrift (Refereegranskat) Published
    Abstract [en]

    A characterization of the distribution of the multivariate quadratic form given by XAX′, where X is a p×n normally distributed matrix and A is an n×n symmetric real matrix, is presented. We show that the distribution of the quadratic form is the same as the distribution of a weighted sum of noncentralWishart distributed matrices. This is applied to derive the distribution of the sample covariance between the rows of X when the expectation is the same for every column and is estimated with the regular mean.

    Ort, förlag, år, upplaga, sidor
    Taylor & Francis, 2012
    Nyckelord
    Quadratic form; Spectral decomposition; Eigenvalues; Singular matrix normal distribution; Non-centralWishart distribution
    Nationell ämneskategori
    Matematik
    Identifikatorer
    urn:nbn:se:liu:diva-18513 (URN)10.1080/03610926.2011.563009 (DOI)000308465400007 ()
    Tillgänglig från: 2009-05-29 Skapad: 2009-05-29 Senast uppdaterad: 2017-12-13
    2. Explicit Estimators under m-Dependence for a Multivariate Normal Distribution
    Öppna denna publikation i ny flik eller fönster >>Explicit Estimators under m-Dependence for a Multivariate Normal Distribution
    2011 (Engelska)Ingår i: Annals of the Institute of Statistical Mathematics, ISSN 0020-3157, E-ISSN 1572-9052, Vol. 63, nr 1, s. 29-42Artikel i tidskrift (Refereegranskat) Published
    Abstract [en]

    The problemof estimating parameters of amultivariate normal p-dimensional random vector is considered for a banded covariance structure reflecting mdependence. A simple non-iterative estimation procedure is suggested which gives an explicit, unbiased and consistent estimator of the mean and an explicit and consistent estimator of the covariance matrix for arbitrary p and m.

    Ort, förlag, år, upplaga, sidor
    Springer, 2011
    Nyckelord
    Banded covariance matrices; Covariance matrix estimation; Explicit estimators; Multivariate normal distribution
    Nationell ämneskategori
    Matematik
    Identifikatorer
    urn:nbn:se:liu:diva-18514 (URN)10.1007/s10463-008-0213-1 (DOI)000286919300002 ()
    Anmärkning
    Preliminary version published as Research Report 2008:3 at the Centre of Biostochastics Swedish University of Agricultural Sciences. The original publication is available at www.springerlink.com: Martin Ohlson, Zhanna Andrushchenko and Dietrich von Rosen, Explicit Estimators under m-Dependence for a Multivariate Normal Distribution, 2011, Annals of the Institute of Statistical Mathematics, (63), 1, 29-42. http://dx.doi.org/10.1007/s10463-008-0213-1 Copyright: Springer Science Business Media http://www.springerlink.com/ Tillgänglig från: 2009-05-29 Skapad: 2009-05-29 Senast uppdaterad: 2017-12-13Bibliografiskt granskad
    3. The Likelihood Ratio Statistic for Testing Spatial Independence using a Separable Covariance Matrix
    Öppna denna publikation i ny flik eller fönster >>The Likelihood Ratio Statistic for Testing Spatial Independence using a Separable Covariance Matrix
    2009 (Engelska)Rapport (Övrigt vetenskapligt)
    Abstract [en]

    This paper deals with the problem of testing spatial independence for dependent observations. The sample observationmatrix is assumed to follow a matrix normal distribution with a separable covariance matrix, in other words it can be written as a Kronecker product of two positive definite matrices. Two cases are considered, when the temporal covariance is known and when it is unknown. When the temporal covariance is known, the maximum likelihood estimates are computed and the asymptotic null distribution is given. In the case when the temporal covariance is unknown the maximum likelihood estimates of the parameters are found by an iterative alternating algori

    Ort, förlag, år, upplaga, sidor
    Linköping: Linköping University Electronic Press, 2009. s. 17
    Serie
    LiTH-MAI-R, ISSN 0348-2960 ; 2009:06
    Nyckelord
    Maximum likelihood estimation, Matrix normal distribution, Testing independence
    Nationell ämneskategori
    Matematik
    Identifikatorer
    urn:nbn:se:liu:diva-18225 (URN)LiTH-MAT-R-2009-06 (ISRN)
    Tillgänglig från: 2009-05-12 Skapad: 2009-05-12 Senast uppdaterad: 2018-10-02Bibliografiskt granskad
    4. Explicit Estimators of Parameters in the Growth Curve Model with Linearly Structured CovarianceMatrices
    Öppna denna publikation i ny flik eller fönster >>Explicit Estimators of Parameters in the Growth Curve Model with Linearly Structured CovarianceMatrices
    2010 (Engelska)Ingår i: Journal of Multivariate Analysis, ISSN 0047-259X, E-ISSN 1095-7243, Vol. 101, nr 5, s. 1284-1295Artikel i tidskrift (Refereegranskat) Published
    Abstract [en]

    Estimation of parameters in the classical Growth Curve model when the covariance matrix has some specific linear structure is considered. In our examples maximum likelihood estimators can not be obtained explicitly and must rely on optimization algorithms. Therefore explicit estimators are obtained as alternatives to the maximum likelihood estimators. From a discussion about residuals, a simple non-iterative estimation procedure is suggested which gives explicit and consistent estimators of both the mean and the linear structured covariance matrix.

    Nyckelord
    Growth Curvemodel; Linearly structured covariancematrix; Explicit estimators; Residuals
    Nationell ämneskategori
    Matematik
    Identifikatorer
    urn:nbn:se:liu:diva-18516 (URN)10.1016/j.jmva.2009.12.023 (DOI)000275504300018 ()
    Anmärkning
    Original Publication: Martin Ohlson and Dietrich von Rosen, Explicit Estimators of Parameters in the Growth Curve Model with Linearly Structured Covariance Matrices, 2010, Journal of Multivariate Analysis, (101), 5, 1284-1295. http://dx.doi.org/10.1016/j.jmva.2009.12.023 Copyright: Elsevier Science B.V., Amsterdam http://www.elsevier.com/ Tillgänglig från: 2009-05-29 Skapad: 2009-05-29 Senast uppdaterad: 2017-12-13Bibliografiskt granskad
  • 36.
    Ohlson, Martin
    Linköpings universitet, Matematiska institutionen, Matematisk statistik. Linköpings universitet, Tekniska högskolan.
    Testing spatial independence using a separable covariance matrix2007Licentiatavhandling, monografi (Övrigt vetenskapligt)
    Abstract [en]

    Spatio-temporal processes like multivariate time series and stochastic processes occur in many applications, for example the observations from functional magnetic resonance imaging (fMRl) or positron emission tomography (PET). It is interesting to test independence between k sets of the variables, that is testing spatial independence.

    This thesis deals with the problem of testing spatial independence for dependent observations. The sample observation matrix is assumed to follow a matrix normal distribution with a separable covariance matrix, in other words it can be written as a Kronecker product of two positive definite matrices. Instead of having a sample observation matrix with independent columns, a covariance between the columns is considered and this covariance matrix is interpreted as a temporal covariance. The main results in this thesis are the computations of the maximum likelihood estimates and the null distribution of the likelihood ratio statistic. Two cases are considered, when the temporal covariance is known and when it is unknown. When the temporal covariance is known, the maximum likelihood estimates are computed and the asymptotic null distribution is shown to be similar to the independent observation case. In the case when the temporal covariance is unknown the maximum likelihood estimates of the parameters are found by an iterative alternating algorithm.

    A well known fact is that when testing hypotheses for covariance matrices, distributions of quadratic forms arise. A generalization of the distribution of the multivariate quadratic form X AX', where X is a (p x n) normally distributed matrix and A is a (n x n) symmetric real matrix, is presented. It is shown that the distribution of the quadratic form is the same as the distribution of a weighted sum of noncentral Wishart distributed matrices.

  • 37.
    Ohlson, Martin
    et al.
    Linköpings universitet, Matematiska institutionen, Matematisk statistik. Linköpings universitet, Tekniska högskolan.
    Ahmad, M. Rauf
    Linköpings universitet, Matematiska institutionen, Matematisk statistik. Linköpings universitet, Tekniska högskolan.
    von Rosen, Dietrich
    Linköpings universitet, Matematiska institutionen, Matematisk statistik. Linköpings universitet, Tekniska högskolan.
    More on the Kronecker Structured Covariance Matrix2012Ingår i: Communications in Statistics - Theory and Methods, ISSN 0361-0926, E-ISSN 1532-415X, Vol. 41, nr 13-14, s. 2512-2523Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    In this paper, the multivariate normal distribution with a Kronecker product structured covariance matrix is studied. Particularly focused is the estimation of a Kronecker structured covariance matrix of order three, the so called double separable covariance matrix. The suggested estimation generalizes the procedure proposed by Srivastava et al. (2008) for a separable covariance matrix. The restrictions imposed by separability and double separability are also discussed.

  • 38.
    Ohlson, Martin
    et al.
    Linköpings universitet, Matematiska institutionen. Linköpings universitet, Tekniska högskolan. Linköpings universitet, Matematiska institutionen, Matematisk statistik.
    Ahmad, M. Rauf
    Linköpings universitet, Matematiska institutionen. Linköpings universitet, Tekniska högskolan.
    von Rosen, Dietrich
    Linköpings universitet, Matematiska institutionen. Linköpings universitet, Tekniska högskolan.
    More on the Kronecker Structured Covariance Matrix2011Rapport (Övrigt vetenskapligt)
    Abstract [en]

    In this paper the multivariate normal distribution with a Kronecker product structured covariance matrix is studied. Particularly, estimation of a Kronecker structured covariance matrix of order three, the so called double separable covariance matrix. The estimation procedure, suggested in this paper, is a generalization of the procedure derived by Srivastava et al. (2008), for a separable covariance matrix.

    Furthermore, the restrictions imposed by separability and double separability are discussed.

  • 39.
    Ohlson, Martin
    et al.
    Linköpings universitet, Matematiska institutionen, Matematisk statistik. Linköpings universitet, Tekniska högskolan.
    Ahmad, M. Rauf
    Linköpings universitet, Matematiska institutionen, Matematisk statistik. Linköpings universitet, Tekniska högskolan.
    von Rosen, Dietrich
    Linköpings universitet, Matematiska institutionen, Matematisk statistik. Linköpings universitet, Tekniska högskolan.
    The Multilinear Normal Distribution: Introduction and Some Basic Properties2013Ingår i: Journal of Multivariate Analysis, ISSN 0047-259X, E-ISSN 1095-7243, Vol. 113, nr S1, s. 37-47Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    In this paper, the multilinear normal distribution is introduced as an extension of the matrix-variate normal distribution. Basic properties such as marginal and conditional distributions, moments, and the characteristic function, are also presented.

    The estimation of parameters using a flip-flop algorithm is also briefly discussed.

  • 40.
    Ohlson, Martin
    et al.
    Linköpings universitet, Matematiska institutionen. Linköpings universitet, Matematiska institutionen, Matematisk statistik. Linköpings universitet, Tekniska högskolan.
    Ahmad, M. Rauf
    Linköpings universitet, Matematiska institutionen. Linköpings universitet, Tekniska högskolan.
    von Rosen, Dietrich
    Linköpings universitet, Matematiska institutionen. Linköpings universitet, Tekniska högskolan.
    The Multilinear Normal Distribution:Introduction and Some Basic Properties2011Rapport (Övrigt vetenskapligt)
    Abstract [en]

    In this paper, the multilinear normal distribution is introduced as an extension of the matrix-variate normal distribution. Basic properties such as marginal and conditional distributions, moments, and the characteristic function, are also presented. The estimation of parameters using a flip-flop algorithm is also briefy discussed.

  • 41.
    Ohlson, Martin
    et al.
    Linköpings universitet, Tekniska högskolan. Linköpings universitet, Matematiska institutionen, Matematisk statistik.
    Andrushchenko, Zhanna
    Department of Biometry and Engineering SLU.
    von Rosen, Dietrich
    Department of Biometry and Engineering SLU.
    Explicit estimators of the parameters in a multivariate normal distribution when the covariance matrix is banded of order m2008Rapport (Övrigt vetenskapligt)
  • 42.
    Ohlson, Martin
    et al.
    Linköpings universitet, Matematiska institutionen, Matematisk statistik. Linköpings universitet, Tekniska högskolan.
    Andrushchenko, Zhanna
    Department of Energy and Technology, Swedish University of Agricultural Sciences, Box 7032, SE–750 07 Uppsala, Sweden.
    von Rosen, Dietrich
    Department of Energy and Technology, Swedish University of Agricultural Sciences, Box 7032, SE–750 07 Uppsala, Sweden.
    Explicit Estimators under m-Dependence for a Multivariate Normal Distribution2011Ingår i: Annals of the Institute of Statistical Mathematics, ISSN 0020-3157, E-ISSN 1572-9052, Vol. 63, nr 1, s. 29-42Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    The problemof estimating parameters of amultivariate normal p-dimensional random vector is considered for a banded covariance structure reflecting mdependence. A simple non-iterative estimation procedure is suggested which gives an explicit, unbiased and consistent estimator of the mean and an explicit and consistent estimator of the covariance matrix for arbitrary p and m.

  • 43.
    Ohlson, Martin
    et al.
    Linköpings universitet, Matematiska institutionen, Matematisk statistik. Linköpings universitet, Tekniska högskolan.
    Koski, Timo
    Royal Institute of Technology, Sweden.
    On the Distribution of Matrix Quadratic Forms2012Ingår i: Communications in Statistics - Theory and Methods, ISSN 0361-0926, E-ISSN 1532-415X, Vol. 41, nr 18, s. 3403-315Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    A characterization of the distribution of the multivariate quadratic form given by XAX′, where X is a p×n normally distributed matrix and A is an n×n symmetric real matrix, is presented. We show that the distribution of the quadratic form is the same as the distribution of a weighted sum of noncentralWishart distributed matrices. This is applied to derive the distribution of the sample covariance between the rows of X when the expectation is the same for every column and is estimated with the regular mean.

  • 44.
    Ohlson, Martin
    et al.
    Linköpings universitet, Matematiska institutionen, Matematisk statistik. Linköpings universitet, Tekniska högskolan.
    Koski, Timo
    Linköpings universitet, Matematiska institutionen, Matematisk statistik. Linköpings universitet, Tekniska högskolan.
    The Likelihood Ratio Statistic for Testing Spatial Independence using a Separable Covariance Matrix2009Rapport (Övrigt vetenskapligt)
    Abstract [en]

    This paper deals with the problem of testing spatial independence for dependent observations. The sample observationmatrix is assumed to follow a matrix normal distribution with a separable covariance matrix, in other words it can be written as a Kronecker product of two positive definite matrices. Two cases are considered, when the temporal covariance is known and when it is unknown. When the temporal covariance is known, the maximum likelihood estimates are computed and the asymptotic null distribution is given. In the case when the temporal covariance is unknown the maximum likelihood estimates of the parameters are found by an iterative alternating algori

  • 45.
    Ohlson, Martin
    et al.
    Linköpings universitet, Matematiska institutionen, Matematisk statistik. Linköpings universitet, Tekniska högskolan.
    Srivastava, Muni S.
    University of Toronto, Department of Statistics.
    Profile Analysis for a Growth Curve Model2010Konferensbidrag (Övrigt vetenskapligt)
    Abstract [en]

    In this talk, we consider profile analysis of several groups where the groups have partly equal means. This leads to a profile analysis for a growth curve model. The likelihood ratio statistics are given for the three hypotheses known in literature as parallelism, level hypothesis and flatness. Furthermore, exact and asymptotic distributions are given in the relavant cases.

     

  • 46.
    Ohlson, Martin
    et al.
    Linköpings universitet, Matematiska institutionen, Matematisk statistik. Linköpings universitet, Tekniska högskolan.
    Srivastava, Muni S.
    University of Toronto, Department of Statistics.
    Profile Analysis for a Growth Curve Model2011Konferensbidrag (Övrigt vetenskapligt)
    Abstract [en]

    In this talk, we consider profile analysis of several groups where subvectors of the mean vectors are equal. This leads to a profile analysis in a growth curve model. The likelihood ratio statistics are given for the three hypotheses known in literature as parallelism, level hypothesis and flatness. Furthermore, exact and asymptotic distributions are given in the relevant cases. 

  • 47.
    Ohlson, Martin
    et al.
    Linköpings universitet, Matematiska institutionen, Matematisk statistik. Linköpings universitet, Tekniska högskolan.
    Srivastava, Muni S.
    Univerity of Toronto, Department of Statistics.
    Profile Analysis for a Growth Curve Model2010Ingår i: Journal of the Japan Statistical Society, ISSN 1882-2754, E-ISSN 1348-6365, Vol. 40, nr 1, s. 1-21Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    In this paper, we consider profile analysis of several groups where the groups have partly equal means. This leads to a profile analysis for a growth curve model. The likelihood ratio statistics are given for the three hypotheses known in literature as parallelism, level hypothesis and flatness. Furthermore, exact and asymptotic distributions are given in the relevant cases.

  • 48.
    Ohlson, Martin
    et al.
    Linköpings universitet, Matematiska institutionen, Matematisk statistik. Linköpings universitet, Tekniska högskolan.
    von Rosen, Dietrich
    Linköpings universitet, Matematiska institutionen, Matematisk statistik. Linköpings universitet, Tekniska högskolan.
    Explicit Estimators of Parameters in the Growth Curve Model with Linearly Structured Covariance Matrices2009Rapport (Övrigt vetenskapligt)
  • 49.
    Ohlson, Martin
    et al.
    Linköpings universitet, Matematiska institutionen, Matematisk statistik. Linköpings universitet, Tekniska högskolan.
    von Rosen, Dietrich
    Linköpings universitet, Matematiska institutionen, Matematisk statistik. Linköpings universitet, Tekniska högskolan.
    Explicit Estimators of Parameters in the Growth Curve Model with Linearly Structured Covariance Matrices2009Konferensbidrag (Övrigt vetenskapligt)
    Abstract [en]

    Estimation of parameters in the classical Growth Curve model when the covariance matrix has some specific linear structure is considered. In our examples maximum likelihood estimators can not be obtained explicitly and must rely on optimization algorithms. Therefore explicit estimators are obtained as alternatives to the maximum likelihood estimators. From a discussion about residuals, a simple non-iterative estimation procedure is suggested which gives explicit and consistent estimators of both the mean and the linear structured covariance matrix.

  • 50.
    Ohlson, Martin
    et al.
    Linköpings universitet, Matematiska institutionen, Matematisk statistik. Linköpings universitet, Tekniska högskolan.
    von Rosen, Dietrich
    Department of Energy and Technology, Swedish University of Agricultural Sciences, Box 7032, SE–750 07 Uppsala, Sweden.
    Explicit Estimators of Parameters in the Growth Curve Model with Linearly Structured CovarianceMatrices2010Ingår i: Journal of Multivariate Analysis, ISSN 0047-259X, E-ISSN 1095-7243, Vol. 101, nr 5, s. 1284-1295Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    Estimation of parameters in the classical Growth Curve model when the covariance matrix has some specific linear structure is considered. In our examples maximum likelihood estimators can not be obtained explicitly and must rely on optimization algorithms. Therefore explicit estimators are obtained as alternatives to the maximum likelihood estimators. From a discussion about residuals, a simple non-iterative estimation procedure is suggested which gives explicit and consistent estimators of both the mean and the linear structured covariance matrix.

12 1 - 50 av 64
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