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Teoriya Veroyatnostei i ee Primeneniya, 2017, Volume 62, Issue 3, Pages 468–498
DOI: https://doi.org/10.4213/tvp5122 (Mi tvp5122) 		 
This article is cited in 10 scientific papers (total in 10 papers)

Asymptotic properties of one-step weighted $M$-estimators with application to some regression problems.

Yu. Yu. Linkeab

a Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences, Novosibirsk
b Novosibirsk State University
Full-text PDF (796 kB) Citations (10)
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DOI: https://doi.org/10.4213/tvp5122
Abstract: 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.
Keywords: one-step $M$-estimators, one-step weighted $M$-estimators, $M$-estimators, asymptotic normality, Newton's iteration method, initial estimator, nonlinear regression.
Received: 07.07.2015
Revised: 08.09.2016
Accepted: 20.02.2017
English version:
Theory of Probability and its Applications, 2018, Volume 62, Issue 3, Pages 373–398
DOI: https://doi.org/10.1137/S0040585X97T988691
Bibliographic databases:
Document Type: Article
Language: Russian
Citation: Yu. Yu. Linke, “Asymptotic properties of one-step weighted $M$-estimators with application to some regression problems.”, Teor. Veroyatnost. i Primenen., 62:3 (2017), 468–498; Theory Probab. Appl., 62:3 (2018), 373–398
Citation in format AMSBIB
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  • https://www.mathnet.ru/eng/tvp/v62/i3/p468
    • This publication is cited in the following 10 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Теория вероятностей и ее применения Theory of Probability and its Applications
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