The Annals of Statistics
- Ann. Statist.
- Volume 25, Number 2 (1997), 495-504.
Convergence of depth contours for multivariate datasets
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.
Ann. Statist., Volume 25, Number 2 (1997), 495-504.
First available in Project Euclid: 12 September 2002
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
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