Asymptotic properties of one-step weighted $M$-estimators and applications to some regression problems

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 $M$-estimators. Sufficient conditions are presented for asymptotic normality of the one-step 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.