SOME NEW RESULTS CONCERNING THE EFFICIENCY OF THE METHOD OF MOMENTS ESTIMATORS FOR THE LOCATION PARAMETER CASE

George Tzavelas (Greece)

Received February 22, 2008

Abstract

In this paper, we study the efficiency of the method of moments estimators for the location parameter and prove that the use of lower moments, results in more efficient estimators compared to the moments obtained with the use of higher moments. For the Normal distribution the loss of efficiency for the estimation of the location parameter with the method of moments tends to zero as the parameter increases to infinity. A case where the optimal estimating function generated by the moments preserves the location parameter structure is studied.

Keywords and phrases: location parameter, estimating function, asymptotic efficiency.