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Improved Nonnegative Estimation of Multivariate Components of Variance

Author

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  • M. S. Srivastava
  • Tatsuya Kubokawa

Abstract

In this paper, we consider a multivariate one-way random effect model with equal replications. We propose non-negative definite estimators for 'between' and 'within' components of variance. Under the Stein loss function/Kullback-Leibler distance function, these estimators are shown to be better than the corresponding unbiased estimators. In particular, it is shown that the proposed restricted maximum likelihood estimator performs better than the unbiased as well as the truncated estimators proposed in this paper. Minimax and order-preserving minimax estimators are also proposed.

Suggested Citation

  • 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.
    • Handle: RePEc:tky:fseres:99cf38
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    Cited by:

    1. Oualkacha Karim & Labbe Aurelie & Ciampi Antonio & Roy Marc-Andre & Maziade Michel, 2012. "Principal Components of Heritability for High Dimension Quantitative Traits and General Pedigrees," Statistical Applications in Genetics and Molecular Biology, De Gruyter, vol. 11(2), pages 1-27, January.
    2. Tatsuya Kubokawa & M. S. Srivastava, 1999. ""Estimating the Covariance Matrix: A New Approach", June 1999," CIRJE F-Series CIRJE-F-52, CIRJE, Faculty of Economics, University of Tokyo.
    3. Wu, Xiaoyong & Zou, Guohua & Li, Yingfu, 2009. "Uniformly minimum variance nonnegative quadratic unbiased estimation in a generalized growth curve model," Journal of Multivariate Analysis, Elsevier, vol. 100(5), pages 1061-1072, May.
    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.
    5. 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.
    6. 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.
    7. Hisayuki Tsukuma & Tatsuya Kubokawa, 2014. "Unified Improvements in Estimation of a Normal Covariance Matrix in High and Low Dimesions," CIRJE F-Series CIRJE-F-937, CIRJE, Faculty of Economics, University of Tokyo.
    8. Tatsuya Kubokawa & M. S. Srivastava, 2002. "Estimating the Covariance Matrix: A New Approach," CIRJE F-Series CIRJE-F-162, CIRJE, Faculty of Economics, University of Tokyo.
    9. Tsai, Ming-Tien, 2007. "Maximum likelihood estimation of Wishart mean matrices under Löwner order restrictions," Journal of Multivariate Analysis, Elsevier, vol. 98(5), pages 932-944, May.

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