Comparison of Risk Ratios of Shrinkage Estimators in High Dimensions

Abstract

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.

On Some Classes of Estimators Derived from the Positive Part of James–Stein Estimator

“…In this model, we will focus on estimating the mean parameters ] using the shrinkage estimators that are based on the BLF. For the quality comparison of any estimator T of ], we incorporate the BLF in the calculation of its risk function as defned in Hamdaoui et al [26].…”