The Annals of Statistics

Convergence of depth contours for multivariate datasets

Xuming He and Gang Wang

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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.

Article information

Source
Ann. Statist., Volume 25, Number 2 (1997), 495-504.

Dates
First available in Project Euclid: 12 September 2002

Permanent link to this document
https://projecteuclid.org/euclid.aos/1031833661

Digital Object Identifier
doi:10.1214/aos/1031833661

Mathematical Reviews number (MathSciNet)
MR1439311

Zentralblatt MATH identifier
0873.62053

Subjects
Primary: 62H12: Estimation
Secondary: 62F35: Robustness and adaptive procedures 62H05: Characterization and structure theory 60H05: Stochastic integrals

Keywords
Convergence contour data depth elliptic distributions location-scatter $M$-estimator multivariate dataset robustness

Citation

He, Xuming; Wang, Gang. Convergence of depth contours for multivariate datasets. Ann. Statist. 25 (1997), no. 2, 495--504. doi:10.1214/aos/1031833661. https://projecteuclid.org/euclid.aos/1031833661


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