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Prediction in Multivariate Mixed Linear Models

Author

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  • Tatsuka Kubokawa

    (Faculty of Economics, University of Tokyo)

  • M. S. Srivastava

    (University of Toronto)

Abstract

The multivariate mixed linear model or multivariate components of variance model with equal replications is considered.The paper addresses the problem of predicting the sum of the regression mean and the random e ects.When the feasible best linear unbiased predictors or empirical Bayes predictors are used,this prediction problem reduces to the estimation of the ratio of two covariance matrices.We propose scale invariant Stein type shrinkage estimators for the ratio of the two covariance matrices.Their dominance properties over the usual estimators including the unbiased one are established, and further domination results are shown by using information of order restriction between the two covariance matrices.It is also demonstrated that the empirical Bayes predictors that employs these improved estimators of the ratio of the two covariance matrices have uniformly smaller risks than the crude Efron-Morris type estimator in the context of estimation of a matrix mean in a xed e ects linear regression model where the components are unknown parameters.

Suggested Citation

  • Tatsuka Kubokawa & M. S. Srivastava, 2002. "Prediction in Multivariate Mixed Linear Models," CIRJE F-Series CIRJE-F-180, CIRJE, Faculty of Economics, University of Tokyo.
    • Handle: RePEc:tky:fseres:2002cf180
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    References listed on IDEAS

    as
    1. Leo Breiman & Jerome H. Friedman, 1997. "Predicting Multivariate Responses in Multiple Linear Regression," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 59(1), pages 3-54.
    2. Konno, Yoshihiko, 1991. "On estimation of a matrix of normal means with unknown covariance matrix," Journal of Multivariate Analysis, Elsevier, vol. 36(1), pages 44-55, January.
    3. Tatsuya Kubokawa & M. S. Srivastava, 1999. "Prediction in Multivariate Mixed Linear Models with Equal Replications," CIRJE F-Series CIRJE-F-62, CIRJE, Faculty of Economics, University of Tokyo.
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