Estimating Parameter of the Selected Uniform Population Under the Generalized Stein Loss Function

This paper deals with the problem of estimating scale parameter of the selected uniform population when sample sizes are unequal. The loss has been measured by the generalized Stein loss (GSL) function. The uniformly minimum risk unbiased (UMRU) estimator is derived, and the natural estimators are also constructed under the GSL function. One of the natural estimators is proved to be the generalized Bayes estimator with respect to a noninformative prior. For k = 2, we obtained a sufficient condition for an inadmissibility result and demonstrate that the natural estimator and UMRU estimator are inadmissible. A simulation investigation is also carried out for the performance of the risk functions of various competing estimators. Finally, this article represents a conclusion of our study.