Uniform asymptotics for robust location estimates when the scale is unknown

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Uniform asymptotics for robust location estimates when the scale is unknown

TitleUniform asymptotics for robust location estimates when the scale is unknown
Publication TypeJournal Article
Year of Publication2004
AuthorsSalibian-Barrera, M, Zamar, RH
JournalANNALS OF STATISTICS
Volume32
Pagination1434-1447
Date PublishedAUG
Type of ArticleArticle
ISSN0090-5364
KeywordsM-estimates, Robust inference, robust location and scale models, Robustness
AbstractMost asymptotic results for robust estimates rely on regularity conditions that are difficult to verily in practice. Moreover, these results apply to fixed distribution functions. In the robustness context the distribution of the data remains largely unspecified and hence results that hold uniformly over a set of possible distribution functions are of theoretical and practical interest. Also, it is desirable to be able to determine the size of the set of distribution functions where the uniform properties hold. In this paper we study the problem of obtaining verifiable regularity conditions that suffice to yield uniform consistency and uniform asymptotic normality for location robust estimates when the scale of the errors is unknown. We study M-location estimates calculated with an S-scale and we obtain uniform asymptotic results over contamination neighborhoods. Moreover, we show how to calculate the maximum size of the contamination neighborhoods where these uniform results hold. There is a trade-off between the size of these neighborhoods and the breakdown point of the scale estimate.
DOI10.1214/009053604000000544