Robust and efficient estimation of the residual scale in linear regression

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Robust and efficient estimation of the residual scale in linear regression

TitleRobust and efficient estimation of the residual scale in linear regression
Publication TypeJournal Article
Year of Publication2013
AuthorsVan Aelst, S, Willems, G, Zamar, RH
JournalJOURNAL OF MULTIVARIATE ANALYSIS
Volume116
Pagination278-296
Date PublishedAPR
Type of ArticleArticle
ISSN0047-259X
KeywordsEfficiency, Gross-error sensitivity, influence function, Maxbias, Robust scale
AbstractRobustness and efficiency of the residual scale estimators in the regression model is important for robust inference. We introduce the class of robust generalized M-scale estimators for the regression model, derive their influence function and gross-error sensitivity, and study their maxbias behavior. In particular, we find overall minimax bias estimates for the general class and also for well-known subclasses. We pose and solve a Hampers-like optimality problem: we find generalized M-scale estimators with maximal efficiency subject to a lower bound on the global and local robustness of the estimators. (C) 2013 Elsevier Inc. All rights reserved.
DOI10.1016/j.jmva.2012.12.008