Uniform asymptotics for S- and MM-regression estimators

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Uniform asymptotics for S- and MM-regression estimators

TitleUniform asymptotics for S- and MM-regression estimators
Publication TypeJournal Article
Year of Publication2010
AuthorsOmelka, M, Salibian-Barrera, M
JournalANNALS OF THE INSTITUTE OF STATISTICAL MATHEMATICS
Volume62
Pagination897-927
Date PublishedOCT
Type of ArticleArticle
ISSN0020-3157
KeywordsRobust inference, Robust regression, Robustness, Uniform asymptotics
AbstractIn this paper we find verifiable regularity conditions to ensure that S-estimators of scale and regression and MM-estimators of regression are uniformly consistent and uniformly asymptotically normally distributed over contamination neighbourhoods. Moreover, we show how to calculate the size of these neighbourhoods. In particular, we find that, for MM-estimators computed with Tukey's family of bisquare score functions, there is a trade-off between the size of these neighbourhoods and both the breakdown point of the S-estimators and the leverage of the contamination that is allowed in the neighbourhood. These results extend previous work of Salibian-Barrera and Zamar for location-scale to the linear regression model.
DOI10.1007/s10463-008-0189-x