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April 2000 General notions of statistical depth function
Robert Serfling, Yijun Zuo
Ann. Statist. 28(2): 461-482 (April 2000). DOI: 10.1214/aos/1016218226


Statistical depth functions are being formulated ad hoc with increasing popularity in nonparametric inference for multivariate data. Here we introduce several general structures for depth functions, classify many existing examples as special cases, and establish results on the possession, or lack thereof, of four key properties desirable for depth functions in general. Roughly speaking, these properties may be described as: affine invariance, maximality at center, monotonicity relative to deepest point, and vanishing at infinity. This provides a more systematic basis for selection of a depth function. In particular, from these and other considerations it is found that the halfspace depth behaves very well overall in comparison with various competitors.


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Robert Serfling. Yijun Zuo. "General notions of statistical depth function." Ann. Statist. 28 (2) 461 - 482, April 2000.


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

zbMATH: 1106.62334
MathSciNet: MR1790005
Digital Object Identifier: 10.1214/aos/1016218226

Primary: 62H05
Secondary: 62G20

Keywords: halfspace depth , multivariate symmetry , simplicial depth , Statistical depth functions

Rights: Copyright © 2000 Institute of Mathematical Statistics


Vol.28 • No. 2 • April 2000
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