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von Rosen, Dietrich
##### Publications (10 of 50) Show all publications
Imori, S. & von Rosen, D. (2019). On the mean and dispersion of the Moore-Penrose generalized inverse of a Wishart matrix. Linköping: Linköping University Electronic Press
Open this publication in new window or tab >>On the mean and dispersion of the Moore-Penrose generalized inverse of a Wishart matrix
2019 (English)Report (Other academic)
##### Abstract [en]

The Moore-Penrose inverse of a singular Wishart matrix is studied. When the scale matrix equals the identity matrix the mean and dispersion matrices of the Moore-Penrose inverse are known. When the scale matrix has an arbitrary structure no exact results are available. We complement the existing literature by deriving upper and lower bounds for the expectation and an upper bound for the dispersion of the Moore-Penrose inverse. The results show that the bounds become large when the number of rows (columns) of the Wishart  matrix are close to the degrees of freedom of the distribution.

##### Place, publisher, year, edition, pages
Linköping: Linköping University Electronic Press, 2019. p. 12
##### Series
LiTH-MAT-R, ISSN 0348-2960 ; 2019:11
##### Keywords
Expectation and dispersion matrix, Moore-Penrose inverse, Wishart matrix
Mathematics
##### Identifiers
urn:nbn:se:liu:diva-161722 (URN)LiTH-MAT-R-2019/11-SE (ISRN)
Available from: 2019-11-07 Created: 2019-11-07 Last updated: 2019-11-07Bibliographically approved
von Rosen, T. & von Rosen, D. (2018). Bilinear regression with random effects and reduced rank restrictions. Linköping: Linköping University Electronic Press
Open this publication in new window or tab >>Bilinear regression with random effects and reduced rank restrictions
2018 (English)Report (Other academic)
##### Abstract [en]

Bilinear models with three types of effects are considered: fixed effects, random effects and latent variable effects. Explicit estimators are proposed.

##### Place, publisher, year, edition, pages
Linköping: Linköping University Electronic Press, 2018. p. 8
##### Series
LiTH-MAT-R, ISSN 0348-2960 ; 2018:8
##### Keywords
Fixed effects, Growth curve model, likelihood based estimates, random effects, rank restrictions
Mathematics
##### Identifiers
urn:nbn:se:liu:diva-149597 (URN)LiTH-MAT-R--2018/08--SE (ISRN)
Available from: 2018-07-09 Created: 2018-07-09 Last updated: 2018-07-16Bibliographically approved
von Rosen, T. & von Rosen, D. (2018). Bilinear regression with rank restrictions on the mean and the dispersion matrix. Linköping: Linköping University Electronic Press
Open this publication in new window or tab >>Bilinear regression with rank restrictions on the mean and the dispersion matrix
2018 (English)Report (Other academic)
##### Abstract [en]

A bilinear regression model with rank restrictions imposed on the mean-parameter matrix and on the dispersion matrix is studied. Maximum likelihood inspired estimates are derived. The approach generalizes classical reduced rank regression analysis and principal component analysis. It is shown via a simulation study and a real example that even for small dimensions the method works as well as reduced rank regression analysis whereas the approach in this article also can be used when the dimension is large.

##### Place, publisher, year, edition, pages
Linköping: Linköping University Electronic Press, 2018. p. 19
##### Series
LiTH-MAT-R, ISSN 0348-2960 ; 2018:10
##### Keywords
Growth curve model, likelihood based estimates, rank restrictions, singular dispersion matrix.
Mathematics
##### Identifiers
urn:nbn:se:liu:diva-150158 (URN)LiTH-MAT-R--2018/10--SE (ISRN)
Available from: 2018-08-14 Created: 2018-08-14 Last updated: 2018-08-14Bibliographically approved
Gauraha, N. & von Rosen, D. (2018). Conditional Independence Models which are Totally Ordered. Linköping: Linköping University Electronic Press
Open this publication in new window or tab >>Conditional Independence Models which are Totally Ordered
2018 (English)Report (Other academic)
##### Abstract [en]

The totally ordered conditional independence (TOCI) model N(K) is defined to be the set of all normal distributions on RI such that for each adjacent pair (Ki, Ki+1) $\in$ K, the components of a multivariate normal vector x $\in$ RI, indexed by the set difference { Ki+1 \ Ki } are mutually conditionally independent given the variables indexed by Ki. Here K = {K1 $\subset$ … $\subset$ Kq } is a totally ordered set of subsets of a finite index set I. It is shown that TOCI models constitute a proper subset of lattice conditional independence (LCI) models. It follows that like LCI models, for the TOCI models the likelihood function and parameter space can be factored into the products of conditional likelihood functions and disjoint parameter spaces, respectively, where each conditional likelihood function corresponds to an ordinary multivariate normal regression model.

##### Place, publisher, year, edition, pages
Linköping: Linköping University Electronic Press, 2018. p. 15
##### Series
LiTH-MAT-R, ISSN 0348-2960 ; 2018:9
Mathematics
##### Identifiers
urn:nbn:se:liu:diva-150009 (URN)LiTH-MAT-R--2018/09--SE (ISRN)
Available from: 2018-08-08 Created: 2018-08-08 Last updated: 2018-10-08Bibliographically 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
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 $\small E[\prod_{i=0}^k Tr\{W^{m_i}\}]$, where $\small W \sim \mathscr{W}_p(I,n)$ denotes a real Wishart matrix. Formulas for fixed n, p  are presented as well as asymptotic versions when $\small \frac{n}{p}\overset{n,p\rightarrow\infty}{\rightarrow}c$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
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
von Rosen, D. & von Rosen, t. (2017). On estimation in some reduced rank extended growth curve models. Mathematical Methods of Statistics, 26(4), 299-310
Open this publication in new window or tab >>On estimation in some reduced rank extended growth curve models
2017 (English)In: Mathematical Methods of Statistics, ISSN 1066-5307, E-ISSN 1934-8045, Vol. 26, no 4, p. 299-310Article in journal (Refereed) Published
##### Abstract [en]

The general multivariate analysis of variance model has been extensively studied in the statistical literature and successfully applied in many different fields for analyzing longitudinal data. In this article, we consider the extension of this model having two sets of regressors constituting a growth curve portion and a multivariate analysis of variance portion, respectively. Nowadays, the data collected in empirical studies have relatively complex structures though often demanding a parsimonious modeling. This can be achieved for example through imposing rank constraints on the regression coefficient matrices. The reduced rank regression structure also provides a theoretical interpretation in terms of latent variables. We derive likelihood based estimators for the mean parameters and covariance matrix in this type of models. A numerical example is provided to illustrate the obtained results.

##### Place, publisher, year, edition, pages
New York, NY, United States: Allerton Press, Inc., 2017
##### Keywords
growth curve model, maximum likelihood estimator, multivariate analysis of variance, reduced rank model
##### National Category
Probability Theory and Statistics
##### Identifiers
urn:nbn:se:liu:diva-152254 (URN)10.3103/S1066530717040044 (DOI)2-s2.0-85039067289 (Scopus ID)
Available from: 2018-10-24 Created: 2018-10-24 Last updated: 2019-01-09Bibliographically approved
Ngaruye, I., von Rosen, D. & Singull, M. (2017). Small area estimation with missing data using a multivariate linear random effects model. Linköping: Linköping University Electronic Press
Open this publication in new window or tab >>Small area estimation with missing data using a multivariate linear random effects model
2017 (English)Report (Other academic)
##### 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
Linköping: Linköping University Electronic Press, 2017. p. 15
##### Series
LiTH-MAT-R, ISSN 0348-2960 ; 2017:07
##### Keywords
Multivariate linear model, Monotone sample, Repeated measures data
##### National Category
Probability Theory and Statistics
##### Identifiers
urn:nbn:se:liu:diva-137648 (URN)LiTH-MAT-R--2017/07--SE (ISRN)
Available from: 2017-05-23 Created: 2017-05-23 Last updated: 2018-01-17Bibliographically approved
Kollo, T., von Rosen, D. & Valge, M. (2016). Hypotheses Testing on Covariance Structures: Comparison of likelihood ratio test, Rao's score test and Wald's score test. In: James R. Bozeman, Teresa Oliveira and Christos H. Skiadas (Ed.), Stochastic and Data Analysis Methods and Applications in Statistics and Demography: . Paper presented at The 16th Conference of the Applied Stochastic Models and Data Analysis International Society, University of Piraeus, Athens, Greece. 30 June - 4 July 2015 (pp. 423-425).
Open this publication in new window or tab >>Hypotheses Testing on Covariance Structures: Comparison of likelihood ratio test, Rao's score test and Wald's score test
2016 (English)In: Stochastic and Data Analysis Methods and Applications in Statistics and Demography / [ed] James R. Bozeman, Teresa Oliveira and Christos H. Skiadas, 2016, p. 423-425Conference paper, Published paper (Refereed)
##### Abstract [en]

For a normal population likelihood ratio test, Rao’s score test and Wald’s score test for testing covariance structures are compared in the situation when the number of variables and the sample size are growing. Expressions of all three test statistics are derived under the general null-hypothesisΣ=Σ0, using matrix derivative techniques. The special casesΣ=γIpandΣ=Ipare also under consideration. The tests are compared in a simulation experiment with sample sizes varying from 100 to 5000 and dimensionalities from 2 to 50. When the number of variables is growing Rao’s score test behaves most adequately.

##### Keywords
Covariance structure, hypotheses testing, likelihood ratio test, Rao’s score test, Wald’s score test
##### National Category
Probability Theory and Statistics
##### Identifiers
urn:nbn:se:liu:diva-152256 (URN)9786185180188 (ISBN)9786185180195 (ISBN)
##### Conference
The 16th Conference of the Applied Stochastic Models and Data Analysis International Society, University of Piraeus, Athens, Greece. 30 June - 4 July 2015
Available from: 2018-10-24 Created: 2018-10-24 Last updated: 2018-11-09Bibliographically approved

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