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

Authors
  • Hara, Hisayuki
Type
Preprint
Publication Date
Oct 05, 2007
Submission Date
Oct 05, 2007
Identifiers
arXiv ID: 0710.1171
Source
arXiv
License
Unknown
External links

Abstract

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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