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John Mwakisisile, A., Larsson, T., Ohlson, M. & Mushi, A. (2018). Asset liability management for Tanzania pension funds by stochastic programming. Afrika Statistika
Open this publication in new window or tab >>Asset liability management for Tanzania pension funds by stochastic programming
2018 (English)In: Afrika Statistika, ISSN 2316-090XArticle in journal (Refereed) Submitted
National Category
Other Mathematics
Identifiers
urn:nbn:se:liu:diva-152118 (URN)
Available from: 2018-10-17 Created: 2018-10-17 Last updated: 2018-10-26Bibliographically approved
Pielaszkiewicz, J., von Rosen, D. & Singull, M. (2018). On n/p-Asymptotic Distribution of Vector of Weighted Traces of Powers of Wishart Matrices. The Electronic Journal of Linear Algebra, 33, 24-40
Open this publication in new window or tab >>On n/p-Asymptotic Distribution of Vector of Weighted Traces of Powers of Wishart Matrices
2018 (English)In: The Electronic Journal of Linear Algebra, ISSN 1537-9582, E-ISSN 1081-3810, Vol. 33, p. 24-40Article in journal (Refereed) Published
Abstract [en]

The joint distribution of standardized traces of $\frac{1}{n}XX'$ and of $\Big(\frac{1}{n}XX'\Big)^2$, where the matrix $X:p\times n$ follows a matrix normal distribution is proved asymptotically to be multivariate normal under condition $\frac{{n}}{p}\overset{n,p\rightarrow\infty}{\rightarrow}c>0$. Proof relies on calculations of asymptotic moments and cumulants obtained using a recursive formula derived in Pielaszkiewicz et al. (2015). The covariance matrix of the underlying vector is explicitely given as a function of $n$ and $p$.

Place, publisher, year, edition, pages
Pensacola, FL, United States: International Linear Algebra Society, 2018
Keywords
Wishart matrix, multivariate normal distribution, spectral distribution, spectral moments, covariance matrix
National Category
Probability Theory and Statistics
Identifiers
urn:nbn:se:liu:diva-152113 (URN)10.13001/1081-3810.3732 (DOI)
Available from: 2018-10-17 Created: 2018-10-17 Last updated: 2019-08-05Bibliographically approved
Ngaruye, I., von Rosen, D. & Ohlson, M. (2018). Small area estimation with missing data using a multivariate linear random effects model. Japanese Journal of Statistics and Data Science
Open this publication in new window or tab >>Small area estimation with missing data using a multivariate linear random effects model
2018 (English)In: Japanese Journal of Statistics and Data Science, ISSN 2520-8756Article in journal (Refereed) Accepted
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.

Place, publisher, year, edition, pages
Springer-Verlag New York, 2018
National Category
Probability Theory and Statistics
Identifiers
urn:nbn:se:liu:diva-147658 (URN)
Available from: 2018-05-03 Created: 2018-05-03 Last updated: 2018-05-09Bibliographically approved
Ngaruye, I., von Rosen, D. & Singull, M. (2017). Mean-squared errors of small area estimators under a multivariate linear model for repeated measures data. Linköping: Linköping University Electronic Press
Open this publication in new window or tab >>Mean-squared errors of small area estimators under a multivariate linear model for repeated measures data
2017 (English)Report (Other academic)
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.

Place, publisher, year, edition, pages
Linköping: Linköping University Electronic Press, 2017. p. 19
Series
LiTH-MAT-R, ISSN 0348-2960 ; 2017:05
Keywords
Mean-squared errors, Multivariate linear model, Repeated measures data, Small area estamation
National Category
Probability Theory and Statistics
Identifiers
urn:nbn:se:liu:diva-137113 (URN)LiTH-MAT-R--2017/05--SE (ISRN)
Available from: 2017-05-05 Created: 2017-05-05 Last updated: 2017-11-02Bibliographically approved
Berntsson, F. & Ohlson, M. (2017). More on Estimation of Banded and Banded Toeplitz Covariance Matrices. Linköping: Linköping University Electronic Press
Open this publication in new window or tab >>More on Estimation of Banded and Banded Toeplitz Covariance Matrices
2017 (English)Report (Other academic)
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.

Place, publisher, year, edition, pages
Linköping: Linköping University Electronic Press, 2017. p. 12
Series
LiTH-MAT-R, ISSN 0348-2960 ; 2017:12
National Category
Probability Theory and Statistics
Identifiers
urn:nbn:se:liu:diva-141051 (URN)LiTH-MAT-R--2017/12--SE (ISRN)
Available from: 2017-09-25 Created: 2017-09-25 Last updated: 2017-10-06Bibliographically approved
Pielaszkiewicz, J., von Rosen, D. & Singull, M. (2017). On E [Pi(k)(i=0) Tr{W-mi}], where W similar to Wp (l, n). Communications in Statistics - Theory and Methods, 46(6), 2990-3005
Open this publication in new window or tab >>On E [Pi(k)(i=0) Tr{W-mi}], where W similar to Wp (l, n)
2017 (English)In: Communications in Statistics - Theory and Methods, ISSN 0361-0926, E-ISSN 1532-415X, Vol. 46, no 6, p. 2990-3005Article in journal (Refereed) Published
Abstract [en]

In this paper, we give a general recursive formula for , where  denotes a real Wishart matrix. Formulas for fixed n, p  are presented as well as asymptotic versions when i.e. when the so called Kolmogorov condition holds. Finally, we show  application of the asymptotic moment relation when deriving moments for the Marchenko-Pastur distribution (free Poisson law). A numerical  illustration using implementation of the main result is also performed.

Place, publisher, year, edition, pages
Taylor & Francis, 2017
Keywords
Eigenvalue distribution; free moments; free Poisson law; Marchenko– Pastur law; random matrices; spectral distribution; Wishart matrix
National Category
Mathematics
Identifiers
urn:nbn:se:liu:diva-122618 (URN)10.1080/03610926.2015.1053942 (DOI)000390425800031 ()
Note

The previous status on this article was Manuscript.

Available from: 2015-11-12 Created: 2015-11-12 Last updated: 2017-12-01Bibliographically approved
Herberthson, M., Johansson, K., Kozlov, V., Ljungkvist, E. & Singull, M. (Eds.). (2017). Proceedings from Workshop: Mathematics in Biology and Medicine, 11-12 May 2017, Linköping University. Paper presented at Workshop: Mathematics in Biology and Medicine, 11-12 May 2017, Linköping University, Sweden. Linköping: Linköping University Electronic Press
Open this publication in new window or tab >>Proceedings from Workshop: Mathematics in Biology and Medicine, 11-12 May 2017, Linköping University
Show others...
2017 (English)Conference proceedings (editor) (Refereed)
Place, publisher, year, edition, pages
Linköping: Linköping University Electronic Press, 2017. p. 27
National Category
Mathematics Other Biological Topics Other Medical Sciences
Identifiers
urn:nbn:se:liu:diva-151460 (URN)
Conference
Workshop: Mathematics in Biology and Medicine, 11-12 May 2017, Linköping University, Sweden
Note

Book of Abstracts.

Available from: 2018-09-21 Created: 2018-09-21 Last updated: 2018-09-25Bibliographically approved
John Mwakisisile, A., Larsson, T., Singull, M. & Mushi, A. (2017). Projecting Tanzania Pension Fund System. African Journal of Applied Statistics, 4(1), 193-218
Open this publication in new window or tab >>Projecting Tanzania Pension Fund System
2017 (English)In: African Journal of Applied Statistics, ISSN 2316-0861, Vol. 4, no 1, p. 193-218Article in journal (Refereed) Published
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.

Place, publisher, year, edition, pages
Afrika Statistika - SPAS, 2017
Keywords
Pension fund; Pay-as-you-go; Defined benefit; Demography
National Category
Probability Theory and Statistics
Identifiers
urn:nbn:se:liu:diva-143272 (URN)10.16929/ajas/2017.193.210 (DOI)
Note

A mandatory Tanzania pension fund with a final salary defined benefit is an- alyzed. 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 anal- ysis 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 possi- ble 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. 

Available from: 2017-11-28 Created: 2017-11-28 Last updated: 2018-08-31Bibliographically approved
Srivastava, M. S. & Singull, M. (2017). Test for the mean matrix in a Growth Curve model for high dimensions. Communications in Statistics - Theory and Methods, 46(13), 6668-6683
Open this publication in new window or tab >>Test for the mean matrix in a Growth Curve model for high dimensions
2017 (English)In: Communications in Statistics - Theory and Methods, ISSN 0361-0926, E-ISSN 1532-415X, Vol. 46, no 13, p. 6668-6683Article in journal (Refereed) Published
Abstract [en]

In this paper we consider the problem of testing (a) sphericity and (b) intraclass covariance structure under a Growth Curve model. The maximum likelihood estimator (MLE) for the mean in a Growth Curve model is a weighted estimator with the inverse of the sample covariance matrix which is unstable for large p close to N and singular for p larger than N. The MLE for the covariance matrix is based on the MLE for the mean, which can be very poor for p close to N. For both structures (a) and (b), we modify the MLE for the mean to an unweighted estimator and based on this estimator we propose a new estimator for the covariance matrix. This new estimator leads to new tests for (a) and (b). We also propose two other tests for each structure, which are just based on the sample covariance matrix.

To compare the performance of all four tests we compute for each structure (a) and (b) the attained significance level and the empirical power. We show that one of the tests based on the sample covariance matrix is better than the likelihood ratio test based on the MLE. 

Place, publisher, year, edition, pages
Taylor & Francis, 2017
Keywords
Growth Curve model; GMANOVA; Sphericity; Intraclass co- variance structure; Hypothesis testing; Asymptotic distribution; Power com- parison; High dimension
National Category
Probability Theory and Statistics
Identifiers
urn:nbn:se:liu:diva-123371 (URN)10.1080/03610926.2015.1132328 (DOI)000398151200030 ()2-s2.0-85015075048 (Scopus ID)
Available from: 2015-12-14 Created: 2015-12-14 Last updated: 2017-04-20Bibliographically approved
Srivastava, M. S. & Ohlson, M. (2017). Testing sphericity and intraclass covariance structures under a Growth Curve model in high dimension. Communications in statistics. Simulation and computation, 46(7), 5740-5751
Open this publication in new window or tab >>Testing sphericity and intraclass covariance structures under a Growth Curve model in high dimension
2017 (English)In: Communications in statistics. Simulation and computation, ISSN 0361-0918, E-ISSN 1532-4141, Vol. 46, no 7, p. 5740-5751Article in journal (Refereed) Published
Abstract [en]

In this article, we consider the problem of testing (a) sphericity and (b) intraclass covariance structure under a growth curve model. The maximum likelihood estimator (MLE) for the mean in a growth curve model is a weighted estimator with the inverse of the sample covariance matrix which is unstable for large p close to N and singular for p larger than N. The MLE for the covariance matrix is based on the MLE for the mean, which can be very poor for p close to N. For both structures (a) and (b), we modify the MLE for the mean to an unweighted estimator and based on this estimator we propose a new estimator for the covariance matrix. This new estimator leads to new tests for (a) and (b). We also propose two other tests for each structure, which are just based on the sample covariance matrix.

To compare the performance of all four tests we compute for each structure (a) and (b) the attained significance level and the empirical power. We show that one of the tests based on the sample covariance matrix is better than the likelihood ratio test based on the MLE.

Place, publisher, year, edition, pages
Taylor & Francis, 2017
Keywords
Asymptotic distribution, GMANOVA, Growth curve model, High dimension, Hypothesis testing, Intraclass covariance structure, Power comparison, Sphericity
National Category
Probability Theory and Statistics
Identifiers
urn:nbn:se:liu:diva-152116 (URN)10.1080/03610918.2016.1175623 (DOI)000410854900046 ()2-s2.0-85015630899 (Scopus ID)
Available from: 2018-10-17 Created: 2018-10-17 Last updated: 2018-11-20Bibliographically approved
Organisations
Identifiers
ORCID iD: ORCID iD iconorcid.org/0000-0001-9896-4438

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