Mean Squared Error Properties of Empirical Bayes Estimators in a Multivariate Random Effects General Linear Model

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Abstract
Estimation of an individual's regression coefficients is considered in a multivariate general linear model, where it is assumed that the individual's coefficients β k are subject to both fixed effects and random effects over different individuals. The mean squared error matrix of a natural estimator of β k is derived for any individual k, in the general situation where all parameters of the model must be estimated, and is shown to be smaller than the mean squared error matrix of the individual least squares estimator for every individual. Extension of this result to more general multiparameter estimation situations is also considered.

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