Asymptotic properties of one-step weighted m-estimators with applications to regression

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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.

Original languageEnglish
Pages (from-to)373-398
Number of pages26
JournalTheory of Probability and its Applications
Issue number3
Publication statusPublished - 1 Jan 2018


  • Asymptotic normality
  • Initial estimator
  • M-estimators
  • Newton’s iteration method
  • Nonlinear regression
  • One-step M-estimators
  • One-step weighted M-estimators

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