Weighted quantile regression with nonelliptically structured covariates

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Weighted quantile regression with nonelliptically structured covariates

TitleWeighted quantile regression with nonelliptically structured covariates
Publication TypeJournal Article
Year of Publication2008
AuthorsSalibian-Barrera, M, Wei, Y
JournalCANADIAN JOURNAL OF STATISTICS-REVUE CANADIENNE DE STATISTIQUE
Volume36
Pagination595-611
Date PublishedDEC
Type of ArticleArticle
ISSN0319-5724
KeywordsNonparametric methods, quantile regression, Robustness
AbstractAlthough quantile regression estimators are robust against low leverage observations with atypically large responses (Koenker & Bassett 1978), they can be seriously affected by a few points that deviate from the majority of the sample covariates. This problem can be alleviated by downweighting observations with high leverage. Unfortunately, when the covariates are not elliptically distributed, Mahalanobis distances may not be able to correctly identify atypical points. In this paper the authors discuss the use of weights based on a new leverage measure constructed using Rosenblatt's multivariate transformation which is able to reflect nonelliptical structures in the covariate space. The resulting weighted estimators are consistent, asymptotically normal, and have a bounded influence function. In addition, the authors also discuss a selection criterion for choosing the downweighting scheme. They illustrate their approach with child growth data from Finland. Finally, their simulation studies suggest that this methodology has good finite-sample properties.