CIRJE-F-187 "Minimax Multivariate Empirical Bayes Estimators under Multicollinearity"
Author Name Srivastava, M. S. and Tatsuya Kubokawa
Date December 2002
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Remarks ‚qevised in January 2004; Subsequently published in Journal of Multivariate Analysis, (2005), 93, 394-416.
Abstract

In this paper we consider the problem of estimating the matrix of regression coefficients in a multivariate linear regression model in which the design matrix is near singular. Under the assumption of normality, we propose empirical Bayes ridge regression estimators with three types of shrinkage functions,that is, scalar, componentwise and matricial shrinkage. These proposed estimators are proved to be uniformly better than the least squares estimator, that is, minimax in terms of risk under the Strawderman's loss function. Through simulation and empirical studies, they are also shown to be useful in the multicollinearity cases.