Pitman closeness comparison of linear estimators:a canonical form

Abstract

A general form is presented for the comparison of two linear estimators of a common parameter by means of the Pitman measure of closeness. Several asymptotic results are given. The case in which the estimators are linear combinations of the order statistics is discussed. The asymptotic comparison of the sample mean versus the sample median is derived for the Laplace distribution, and two other examples are given.

Keywords:

• Pitman's measure of closeness
• order statistics
• Laplace distribution