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We study asymptotic behavior of one-step $M$-estimators based on samples fromarrays of not necessarily identically distributed random variables andrepresenting explicit approximations to the corresponding consistent$M$-estimators. These estimators generalize Fisher's one-step approximations toconsistent maximum likelihood estimators. As a consequence, we consider somenonlinear regression problems where the procedure mentioned allow us toconstruct explicit asymptotically optimal estimators. We also consider theproblem of constructing initial estimators which are needed for one-stepestimation procedures.

Asymptotic properties of one-step $M$-estimators based on nonidentically distributed observations with applications to nonlinear regression problems