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

Abstract

We study asymptotic behavior of one-step weighted M-estimators based on samples from arrays of not necessarily identically distributed random variables and representing explicit approximations to the corresponding consistent weighted Mestimators. Sufficient conditions are presented for asymptotic normality of the onestep weighted M-estimators under consideration. As a consequence, we consider some well-known nonlinear regression models where the procedure mentioned allow us to construct explicit asymptotically optimal estimators.