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October 1999 Asymptotic distributions of the maximal depth estimators for regression and multivariate location
Zhi-Dong Bai, Xuming He
Ann. Statist. 27(5): 1616-1637 (October 1999). DOI: 10.1214/aos/1017939144

Abstract

We derive the asymptotic distribution ofthe 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.

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Zhi-Dong Bai. Xuming He. "Asymptotic distributions of the maximal depth estimators for regression and multivariate location." Ann. Statist. 27 (5) 1616 - 1637, October 1999. https://doi.org/10.1214/aos/1017939144

Information

Published: October 1999
First available in Project Euclid: 23 September 2004

zbMATH: 1007.62009
MathSciNet: MR2001G:62035
Digital Object Identifier: 10.1214/aos/1017939144

Subjects:
Primary: 62F12, 62G35
Secondary: 62H12, 62J05

Rights: Copyright © 1999 Institute of Mathematical Statistics

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Vol.27 • No. 5 • October 1999
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