Open Access
Translator Disclaimer
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


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.


Download Citation

Xuming He. Gang Wang. "Convergence of depth contours for multivariate datasets." Ann. Statist. 25 (2) 495 - 504, April 1997.


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

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

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

Keywords: $M$-estimator , contour , convergence , data depth , elliptic distributions , location-scatter , multivariate dataset , robustness

Rights: Copyright © 1997 Institute of Mathematical Statistics


Vol.25 • No. 2 • April 1997
Back to Top