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Improved Nonnegative Estimation of Multivariate Components of Variance


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  • M. S. Srivastava
  • Tatsuya Kubokawa
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    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.

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    Bibliographic Info

    Paper provided by CIRJE, Faculty of Economics, University of Tokyo in its series CIRJE F-Series with number CIRJE-F-38.

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    Length: 20 pages
    Date of creation: Jan 1999
    Date of revision:
    Handle: RePEc:tky:fseres:99cf38

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    Cited by:
    1. Tatsuya Kubokawa & M. S. Srivastava, 2002. "Estimating the Covariance Matrix: A New Approach," CIRJE F-Series, CIRJE, Faculty of Economics, University of Tokyo CIRJE-F-162, CIRJE, Faculty of Economics, University of Tokyo.
    2. 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.
    3. Tatsuya Kubokawa & M. S. Srivastava, 1999. ""Estimating the Covariance Matrix: A New Approach", June 1999," CIRJE F-Series, CIRJE, Faculty of Economics, University of Tokyo CIRJE-F-52, CIRJE, Faculty of Economics, University of Tokyo.


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