One-Step $L$-Estimators for the Linear Model

Abstract

We propose and investigate the asymptotic properties of a class of estimators of the regression parameter in the general linear model. The estimators depend on a preliminary estimate of the regression parameter and the residuals based on it. For the location model, the estimators are linear combinations of the order statistics and the robustness and efficiency properties of this class of estimators carry over to the general linear model. The estimators settle the doubts raised by Bickel (1973) about the feasibility of the construction of a general class of reparametrization invariant estimators of a regression parameter which are linear combinations of order statistics in the location problem.