Minimax variance M-estimators in \(\epsilon\)-contamination models
type: Item
instance of: scholarly article
title: Minimax variance M-estimators in \(\epsilon\)-contamination models
zbMATH Open document ID: 0584.62049
author: John R. Collins
author: Douglas P. Wiens
published in: The Annals of Statistics
publication date: 1985-01-01T00:00:00Z
review text: The problem of estimation of a location parameter is considered, when the \(\epsilon\)-contamination model \(f(x)=(1-\epsilon)h(x)+\epsilon g(x)\) is used. The authors investigate the form of the minimax variance solutions. Differently from the well-known result of \textit{P. J. Huber} [Ann. math. Stat. 35, 73-101 (1964; Zbl 0136.398)], the known density h is not necessarily strongly unimodal, and definite results are obtained under mild regularity conditions on h. Minimax variance problems for multivariate location and scale parameters are also studied.
Mathematics Subject Classification ID: 62F35
Mathematics Subject Classification ID: 62F12
Mathematics Subject Classification ID: 62H12
zbMATH DE Number: 3936208
zbMATH Keywords: robust estimation
zbMATH Keywords: M-estimators
zbMATH Keywords: epsilon contamination
zbMATH Keywords: minimax variance solutions
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1214/aos/1176349657
OpenAlex ID: W2029419002
DOI: 10.1214/AOS/1176349657
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description: scientific article; zbMATH DE number 3936208