Bootstrapping MM-estimators for linear regression with fixed designs

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Bootstrapping MM-estimators for linear regression with fixed designs

TitleBootstrapping MM-estimators for linear regression with fixed designs
Publication TypeJournal Article
Year of Publication2006
AuthorsSalibian-Barrera, M
JournalSTATISTICS & PROBABILITY LETTERS
Volume76
Pagination1287-1297
Date PublishedJUL 1
Type of ArticleArticle
ISSN0167-7152
Keywordsbootstrap, fixed design, inference, linear regression, MM-estimators, Robustness
AbstractIn this paper, I study the extension of the robust bootstrap [Salibian-Barrera, M., Zarnar, R.H., 2002. Bootstrapping robust estimates of regression. Ann. Statist. 30, 556-582] to the case of fixed designs. The robust bootstrap is a computer-intensive inference method for robust regression estimators which is computationally simple (because we do not need to recompute the robust estimate with each bootstrap sample) and robust to the presence of outliers in the bootstrap samples. In this paper, I prove the consistency of this method for the case of non-random explanatory variables and illustrate its use on a real data set. Simulation results indicate that confidence intervals based on the robust bootstrap have good finite-sample coverage levels. (C) 2006 Elsevier B.V. All rights reserved.
DOI10.1016/j.spl.2006.01.008