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

TL;DR

This paper introduces improved nonnegative estimators for the MSEs and MSE matrices of shrinkage estimators in multivariate normal models, enhancing accuracy and practical confidence set construction.

Contribution

It proposes novel nonnegative and positive estimators that outperform the UMVUE for MSEs and MSE matrices, with applications to confidence set formation.

Findings

Proposed estimators improve on the UMVUE under quadratic loss.

Enhanced estimators lead to more accurate confidence sets.

Numerical experiments demonstrate practical usefulness.

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.