Principal components analysis based on multivariate MM estimators with fast and robust bootstrap

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Principal components analysis based on multivariate MM estimators with fast and robust bootstrap

TitlePrincipal components analysis based on multivariate MM estimators with fast and robust bootstrap
Publication TypeJournal Article
Year of Publication2006
AuthorsSalibian-Barrera, M, Van Aelst, S, Willems, G
JournalJOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION
Volume101
Pagination1198-1211
Date PublishedSEP
Type of ArticleArticle
ISSN0162-1459
Keywordsbootstrap, inference, MM-estimators, Principal components, Robustness
AbstractWe consider robust principal components analysis (PCA) based on multivariate MM estimators. We first study the robustness and efficiency of these estimators, particularly in terms of eigenvalues and eigenvectors. We then focus on inference procedures based on a fast and robust bootstrap for MM estimators. This method is an alternative to the approach based on the asymptotic distribution of the estimators and can also be used to assess the stability of the principal components. A formal consistency proof for the bootstrap method is given, and its finite-sample performance is investigated through simulations. We illustrate the use of the robust PCA and the bootstrap inference on a real dataset.
DOI10.1198/016214506000000096