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Title: Asymptotic distributions of the maximal depth estimators for regression and multivariate location
Authors: Bai, Z.-D. 
He, X.
Keywords: Asymptotic distribution
Multivariate location
Regression depth
Issue Date: Oct-1999
Citation: Bai, Z.-D.,He, X. (1999-10). Asymptotic distributions of the maximal depth estimators for regression and multivariate location. Annals of Statistics 27 (5) : 1616-1637. ScholarBank@NUS Repository.
Abstract: We derive the asymptotic distribution of the maximal depth regression estimator recently proposed in Rousseeuw and Hubert. The estimator is obtained by maximizing a projection-based depth and the limiting distribution is characterized through a max - min operation of a continuous process. The same techniques can be used to obtain the limiting distribution of some other depth estimators including Tukey's deepest point based on half-space depth. Results for the special case of two-dimensional problems have been available, but the earlier arguments have relied on some special geometric properties in the low-dimensional space. This paper completes the extension to higher dimensions for both regression and multivariate location models.
Source Title: Annals of Statistics
ISSN: 00905364
Appears in Collections:Staff Publications

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