Prediction in Multivariate Mixed Linear Models

Tatsuka Kubokawa and M. S. Srivastava
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Tatsuka Kubokawa: Faculty of Economics, University of Tokyo
M. S. Srivastava: University of Toronto

No CIRJE-F-180, CIRJE F-Series from CIRJE, Faculty of Economics, University of Tokyo

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.

Pages: 25 pages
Date: 2002-10
New Economics Papers: this item is included in nep-ecm
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Persistent link: https://EconPapers.repec.org/RePEc:tky:fseres:2002cf180

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