A new approach for shrinkage estimators of the multivariate normal mean vector under the balanced loss criterion

In this study, we investigate the issue of estimating the mean vector of a multivariate normal distribution. We introduce two new families of shrinkage estimators derived from both the maximum likelihood estimator and the James-Stein estimator. To evaluate their performance, we employ the risk function associated with the balanced loss criterion. Using this criterion, we establish that these estimators consistently outperform the positive part of the James-Stein estimator. Furthermore, we show that the estimators from the second family exhibit better performance than those from the first. Finally, we conclude with simulation studies that confirm our theoretical findings.