The asymptotics of MM-estimators for linear regression with fixed designs

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The asymptotics of MM-estimators for linear regression with fixed designs

TitleThe asymptotics of MM-estimators for linear regression with fixed designs
Publication TypeJournal Article
Year of Publication2006
AuthorsSalibian-Barrera, M
JournalMETRIKA
Volume63
Pagination283-294
Date PublishedJUN
Type of ArticleArticle
ISSN0026-1335
Keywordsasymptotic distribution, consistency, fixed designs, MM-estimators
AbstractMM-estimators achieve simultaneous high efficiency and high breakdown point over contamination neighborhoods. Inference based on these estimators relies on their asymptotic properties, which have been studied for the case of random covariates. In this paper we show that, under relatively mild regularity conditions, MM-estimators for linear regression models are strongly consistent when the design is fixed. Moreover, their strong consistency allows us to show that these estimators are also asymptotically normal for non-random covariates. These results justify the use of a normal approximation to the finite-sample distribution of MM-estimators for linear regression with fixed explanatory variables. Additionally, these results have been used to extend the robust bootstrap (Salibian-Barrera and Zamar in Ann Stat 30:556-582, 2002) to the case of fixed designs [see Salibian-Barrera 2004, submitted].
DOI10.1007/s00184-005-0019-6