On Estimating Scale Parameter of the Selected Pareto Population under the Generalized Stein Loss Function

Abstract

The problem of estimation after selection can be seen in numerous statistical applications. Let be a random sample drawn from the population where Π i follows Pareto distribution with an unknown scale parameter θi and common known shape parameter β. This article is concerned with the problem of estimating θL (or θS ), the scale parameter of the selected Pareto population under the generalized Stein loss function. The uniformly minimum risk unbiased (UMRU) estimators of θL and θS , scale parameters of the largest and the smallest population respectively, are determined. For k = 2, we have obtained a sufficient condition of minimaxity of θS and showed that the generalized Bayes estimator of θS is a minimax estimator for k = 2. Also, a class of linear admissible estimators of the form of θL and θS is found, and a sufficient condition for inadmissibility is provided. Further, we demonstrate that the UMRU estimator of θS is inadmissible. A comparison between the proposed estimators is conducted using MATLAB software and a real data set is analyzed for illustrative purposes. Finally, conclusions and discussion are reported.