Minimax Estimation of the Scale Parameter in a Family of Transformed Chi-Square Distributions under Asymmetric Squared Log Error and MLINEX Loss Functions

Abstract

This paper is concerned with the problem of finding the minimax estimators of the scale parameter ? in a family of transformed chi-square distributions, under asymmetric squared log error (SLE) and modified linear exponential (MLINEX) loss functions, using the Lehmann Theorem [2]. Also we show that the results of Podder et al. [4] for Pareto distribution are a special case of our results for this family of distributions.