Pitman Closest Estimators Based on Convex Linear Combinations of Two Contiguous Order Statistics

Abstract

Comparisons of best linear unbiased estimators with some other prominent estimators have been carried out over the last six decades since the ground breaking work of Lloyd [13]; see Arnold et al. [1] and David and Nagaraja [9] for elaborate details in this regard. Recently, Pitman closeness comparison of order statistics as estimators for population parameters, such as medians and quantiles, and their applications have been carried out by Balakrishnan et al. [3, 4, 5, 7]. In this paper, we discuss the Pitman closest estimators based on convex linear combinations of two contiguous order statistics, which sheds additional insight with regard to the estimation of the population median in the case of even sample sizes. We finally demonstrate the proposed method for the uniform, exponential, power function and Pareto distributions.