Asymptotic properties of one-step M-estimators

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Abstract

We study the asymptotic behavior of one-step M-estimators based on not necessarily independent identically distributed observations. In particular, we find conditions for asymptotic normality of these estimators. Asymptotic normality of one-step M-estimators is proven under a wide spectrum of constraints on the exactness of initial estimators. We discuss the question of minimal restrictions on the exactness of initial estimators. We also discuss the asymptotic behavior of the solution to an M-equation closest to the parameter under consideration. As an application, we consider some examples of one-step approximation of quasi-likelihood estimators in nonlinear regression.

Original languageEnglish
Pages (from-to)4096-4118
Number of pages23
JournalCommunications in Statistics - Theory and Methods
Volume48
Issue number16
DOIs
Publication statusPublished - 18 Aug 2019

Keywords

  • asymptotic normality
  • initial estimator
  • nonlinear regression
  • One-step M-estimator
  • REGRESSION
  • HIGH BREAKDOWN
  • INFERENCES
  • MODELS
  • NORMALITY
  • BEHAVIOR
  • ROOTS
  • EFFICIENT ESTIMATION

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