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Estimation of covariance matrices in fixed and mixed effects linear models

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  • Kubokawa, Tatsuya
  • Tsai, Ming-Tien

Abstract

The estimation of the covariance matrix or the multivariate components of variance is considered in the multivariate linear regression models with effects being fixed or random. In this paper, we propose a new method to show that usual unbiased estimators are improved on by the truncated estimators. The method is based on the Stein-Haff identity, namely the integration by parts in the Wishart distribution, and it allows us to handle the general types of scale-equivariant estimators as well as the general fixed or mixed effects linear models.

Suggested Citation

  • Kubokawa, Tatsuya & Tsai, Ming-Tien, 2006. "Estimation of covariance matrices in fixed and mixed effects linear models," Journal of Multivariate Analysis, Elsevier, vol. 97(10), pages 2242-2261, November.
  • Handle: RePEc:eee:jmvana:v:97:y:2006:i:10:p:2242-2261
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    References listed on IDEAS

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    1. Mathew, T. & Niyogi, A. & Sinha, B. K., 1994. "Improved Nonnegative Estimation of Variance Components in Balanced Multivariate Mixed Models," Journal of Multivariate Analysis, Elsevier, vol. 51(1), pages 83-101, October.
    2. Haff, L. R., 1979. "An identity for the Wishart distribution with applications," Journal of Multivariate Analysis, Elsevier, vol. 9(4), pages 531-544, December.
    3. M. S. Srivastava & Tatsuya Kubokawa, 1999. "Improved Nonnegative Estimation of Multivariate Components of Variance," CIRJE F-Series CIRJE-F-38, CIRJE, Faculty of Economics, University of Tokyo.
    4. Kubokawa, T. & Srivastava, M. S., 2003. "Estimating the covariance matrix: a new approach," Journal of Multivariate Analysis, Elsevier, vol. 86(1), pages 28-47, July.
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    Cited by:

    1. Tsukuma, Hisayuki & Kubokawa, Tatsuya, 2016. "Unified improvements in estimation of a normal covariance matrix in high and low dimensions," Journal of Multivariate Analysis, Elsevier, vol. 143(C), pages 233-248.
    2. Tsai, Ming-Tien & Kubokawa, Tatsuya, 2007. "Estimation of Wishart mean matrices under simple tree ordering," Journal of Multivariate Analysis, Elsevier, vol. 98(5), pages 945-959, May.

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