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April 1997 Convergence of depth contours for multivariate datasets
Xuming He, Gang Wang
Ann. Statist. 25(2): 495-504 (April 1997). DOI: 10.1214/aos/1031833661

Abstract

Contours of depth often provide a good geometrical understanding of the structure of a multivariate dataset. They are also useful in robust statistics in connection with generalized medians and data ordering. If the data constitute a random sample from a spherical or elliptic distribution, the depth contours are generally required to converge to spherical or elliptical shapes. We consider contour constructions based on a notion of data depth and prove a uniform contour convergence theorem under verifiable conditions on the depth measure. Applications to several existing depth measures discussed in the literature are also considered.

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Xuming He. Gang Wang. "Convergence of depth contours for multivariate datasets." Ann. Statist. 25 (2) 495 - 504, April 1997. https://doi.org/10.1214/aos/1031833661

Information

Published: April 1997
First available in Project Euclid: 12 September 2002

zbMATH: 0873.62053
MathSciNet: MR1439311
Digital Object Identifier: 10.1214/aos/1031833661

Subjects:
Primary: 62H12
Secondary: 60H05, 62F35, 62H05

Rights: Copyright © 1997 Institute of Mathematical Statistics

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Vol.25 • No. 2 • April 1997
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