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April 2000 Structural properties and convergence results for contours of sample statistical depth functions
Robert Serfling, Yijun Zuo
Ann. Statist. 28(2): 483-499 (April 2000). DOI: 10.1214/aos/1016218227


Statistical depth functions have become increasingly used in nonparametric inference for multivariate data. Here the contours of such functions are studied. Structural properties of the regions enclosed by contours, such as affine equivariance, nestedness, connectedness and compactness, and almost sure convergence results for sample depth contours, are established. Also, specialized results are established for some popular depth functions, includinghalfspace depth, and for the case of elliptical distributions. Finally, some needed foundational results on almost sure convergence of sample depth functions are provided.


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Robert Serfling. Yijun Zuo. "Structural properties and convergence results for contours of sample statistical depth functions." Ann. Statist. 28 (2) 483 - 499, April 2000.


Published: April 2000
First available in Project Euclid: 15 March 2002

zbMATH: 1105.62343
MathSciNet: MR1790006
Digital Object Identifier: 10.1214/aos/1016218227

Primary: 62H12
Secondary: 62G20

Keywords: Almost sure convergence , depth contours , elliptical distributions , halfspace depth , sample depth contours , Statistical depth functions

Rights: Copyright © 2000 Institute of Mathematical Statistics


Vol.28 • No. 2 • April 2000
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