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.
Highlights
We extended the work to study the limit of the risk ratios of the James–Stein estimator to the maximum likelihood estimator (MLE) when d tends to infinity
We study the superiority of the positive-part version of the James–Stein estimator to the James–Stein estimator, and the limit of the risk ratio of the positive-part version of the James–Stein estimator to the MLE when the dimension of the parameter space d tends to infinity
Lim namely, the positive-part version of James–Stein estimator TJ.S+ dominates the MLE, even if d tends to infinity
Summary
Publisher’s Note: MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations When it comes to estimating the mean parameter of a multivariate normal distribution, the minimax technique has attracted the greatest attention and development in research far. Enhancing estimators has been accomplished through the development of shrinkage estimators that minimize the risk associated with the quadratic loss function. Using the generalized Bayes shrinkage estimators of location parameter for a spherical distribution subject to a balance-type loss, Karamikabir et al [20] determined the minimax and acceptable estimators of the location parameter. We discuss the positive-part version of the James–Stein estimator and the asymptotic behavior of its risk ratios to the MLE in scenarios where the dimension of the parameter space d is either finite or goes to infinity. We end this paper with the results of a simulation study, which illustrate the performance of the considered estimators
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