| 1. |
- Ohlson, Martin, 1977-, et al.
(författare)
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More on the Kronecker Structured Covariance Matrix
- 2012
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Ingår i: Communications in Statistics - Theory and Methods. - : Taylor & Francis. - 0361-0926 .- 1532-415X. ; 41:13-14, s. 2512-2523
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Tidskriftsartikel (refereegranskat)abstract
- 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.
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| 2. |
- Singull, Martin, 1977-, et al.
(författare)
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On the Distribution of Matrix Quadratic Forms
- 2012
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Ingår i: Communications in Statistics - Theory and Methods. - : Informa UK Limited. - 0361-0926 .- 1532-415X. ; 41:18, s. 3403-3415
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Tidskriftsartikel (refereegranskat)abstract
- A characterization of the distribution of the multivariate quadratic form given by XAX', where X is a p x n normally distributed matrix and A is an n x 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 non central Wishart 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.
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| 3. |
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| 4. |
- Berntsson, Fredrik, 1971-, et al.
(författare)
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More on Estimation of Banded and Banded Toeplitz Covariance Matrices
- 2017
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Rapport (övrigt vetenskapligt/konstnärligt)abstract
- 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.
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| 5. |
- John Mwakisisile, Andongwisye, et al.
(författare)
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Asset liability management for Tanzania pension funds by stochastic programming
- 2018
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Ingår i: Afrika Statistika. - : The Statistics and Probability African Society Discipline(s). - 2316-090X. ; 13:3, s. 1733-1758
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Tidskriftsartikel (refereegranskat)abstract
- We present a long-term model of asset liability management for Tanzania pension funds. The pension system is pay-as-you-go where contributions are used to pay current benefits. The pension plan is a final salary defined benefit. Two kinds of pension benefits, a commuted (at retirement) and a monthly (old age) pension are considered. A decisive factor for a long-term asset liability management is that, Tanzania pension funds face an increase of their members’ life expectancy, which will cause the retirees to contributors dependence ratio to increase. We present a stochastic programming approach which allocates assets with the best return to raise the asset value closer to the level of liabilities. The model is based on work by Kouwenberg in 2001, with features from Tanzania pension system. In contrast to most asset liability management models for pension funds by stochastic programming, liabilities are modeled by using number of years of life expectancy for monthly benefit. Scenario trees are generated by using Monte Carlo simulation. Numerical results suggest that, in order to improve the long-term sustainability of the Tanzania pension fund system, it is necessary to make reforms concerning the contribution rate, investment guidelines and formulate target funding ratios to characterize the pension funds’ solvency situation.
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| 6. |
- Ngaruye, Innocent, et al.
(författare)
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Small area estimation with missing data using a multivariate linear random effects model
- 2018
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Ingår i: Japanese Journal of Statistics and Data Science. - : Springer-Verlag New York. - 2520-8756 .- 2520-8764. ; 1, s. 23-37
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Tidskriftsartikel (refereegranskat)abstract
- 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.
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| 7. |
- Ohlson, Martin, 1977-
(författare)
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Distribution of Quadratic Forms
- 2007
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Konferensbidrag (övrigt vetenskapligt/konstnärligt)abstract
- 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.
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| 8. |
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| 9. |
- Ohlson, Martin, 1977-, et al.
(författare)
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Explicit Estimators of Parameters in the Growth Curve Model with Linearly Structured Covariance Matrices
- 2009
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Konferensbidrag (övrigt vetenskapligt/konstnärligt)abstract
- 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.
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| 10. |
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