In this approach, we construct the necessary and sufficient conditions in order a James-Stein type estimator outperforms the minimax estimator of the mean. Particularly we consider a class of spherically symmetric distributions and derive the dominating conditions under the quartic loss function. Multivariate Student's t and Slash distributions as two examples are also considered for checking the efficiency of the proposed model and specifying theoretical requirements.

Keywords: Elliptically Contoured Distribution; James-Stein Estimator; Quartic Loss Function; Spherically Symmetric Distribution

Biography: Dr. Mohammad Arashi, is an Assistant Professor in Faculty of Mathematics, Shahrood University of Technology, Iran. He is particularly interested in shrinkage estimation and elliptically contoured models.