We study asymptotic behavior of one-step $M$-estimators based on samples from arrays of not necessarily identically distributed random variables and representing explicit approximations to the corresponding consistent $M$-estimators. These estimators generalize Fisher's one-step approximations to consistent maximum likelihood estimators. Sufficient conditions are presented for asymptotic normality of the one-step $M$-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.
Asymptotic properties of one-step weighted $M$-estimators and applications to some regression problems
Iterative estimating equations: Linear convergence and asymptotic properties
Asymptotic properties of spiked eigenvalues and eigenvectors of signal-plus-noise matrices with their applications
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