On the Shrinkage Estimators for a Multivariate Normal Mean Vector with Unknown Diagonal Covariance Matrix

Abstract

The results presented in this work focus on the construction of two classes of shrinkage estimators for a Multivariate Normal Mean (MNM) and studying their performance according to the Balanced Loss Function (BLF). First, we introduce a class of estimators derived from the Maximum Likelihood Estimator (MLE) and provide a sufficient condition on the shrinkage function to improve upon the MLE. Then, from the MLE and the James-Stein Estimator (JSE) we build a new class of estimators, and under a simple practical condition, we show that their risks are no greater than those of the JSE, which explains why they perform better. We conclude the paper with numerical results that confirm the performance of the proposed estimators.