Minimax Multivariate Empirical Bayes Estimators under Multicollinearity

Tatsuya Kubokawa and M. S. Srivastava
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Tatsuya Kubokawa: Faculty of Economics, University of Tokyo
M. S. Srivastava: Department of Statistics, University of Toronto

No CIRJE-F-187, CIRJE F-Series from CIRJE, Faculty of Economics, University of Tokyo

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.

Pages: 22 pages
Date: 2002-12
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Persistent link: https://EconPapers.repec.org/RePEc:tky:fseres:2002cf187

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