Comparison of Risk Ratios of Shrinkage Estimators in High Dimensions

In this paper, we analyze the risk ratios of several shrinkage estimators using a balanced loss function. The James-Stein estimator is one of a group of shrinkage estimators that has been proposed in the existing literature. For these estimators, sufficient criteria for minimaxity have been established, and the James-Stein estimator's minimaxity has been derived. We demonstrate that the James-Stein estimator's minimaxity is still valid even when the parameter space has infinite dimension. It is shown that the positive-part version of the James-Stein estimator is substantially superior to the James-Stein estimator, and we address the asymptotic behavior of their risk ratios to the maximum likelihood estimator (MLE) when the dimensions of the parameter space are infinite. Finally, a simulation study is carried out to verify the performance evaluation of the considered estimators.