Asymptotic Properties of One-Step Weighted $M$-Estimators with Applications to Regression

Abstract

We study the asymptotic behavior of one-step weighted $M$-estimators based on independent not necessarily identically distributed observations, which approximate consistent weighted $M$-estimators. We find sufficient conditions for asymptotic normality of these estimators. As an application, we consider some known regression models where the one-step estimation under consideration allows us to construct explicit asymptotically optimal estimators having the same accuracy as the least-squares or quasi-likelihood estimators.