Improved estimation of the MSEs and the MSE matrices for shrinkage estimators of multivariate normal means and their applications

Details Improved estimation of the MSEs and the MSE matrices for shrinkage estimators of multivariate normal means and their applications Improved estimation of the MSEs and the MSE matrices for shrinkage estimators of multivariate normal means and their applications

2007-10-05

arxiv.org/abs/0710.1171v1

Mathematics

Statistics Theory

29 pages

Scientific paper

In this article we provide some nonnegative and positive estimators of the mean squared errors(MSEs) for shrinkage estimators of multivariate normal means. Proposed estimators are shown to improve on the uniformly minimum variance unbiased estimator(UMVUE) under a quadratic loss criterion. A similar improvement is also obtained for the estimators of the MSE matrices for shrinkage estimators. We also apply the proposed estimators of the MSE matrix to form confidence sets centered at shrinkage estimators and show their usefulness through numerical experiments.

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