Adjusted Non-Linear Unbiased Estimation of the Location Parameter of a Symmetric Distribution

Abstract

In this paper we consider a location family of distributions which are symmetric about the location parameter μ and propose a nonlinear function of order statistics as an estimator of μ. We call this estimator as the adjusted non-linear unbiased estimator of μ. For the U-shaped distribution with location parameter μ, we have illustrated that our estimator is a competitor of $\widehat{\mu }$ , the best linear unbiased estimator of μ based on order statistics. We have also identified the region of the parameter space in which the proposed estimator is more efficient than $\widehat{\mu }$ .