Edgeworth expansions for M-estimators of a regression parameter

Abstract

This paper gives rth order Edgeworth expansions ( r ≥ 3) for M-estimators of a regression parameter in a simple linear regression model. The regularity conditions used here essentially require the smoothness of some integrals of the score function with respect to the underlying error distribution. As a result, these expansions are valid for robust M-estimators corresponding to nonsmooth score functions.