Smooth depth contours characterize the underlying distribution

Authors:
Linglong Kong;Yijun Zuo
Affiliations:
Department of Statistics and Probability, Michigan State University, East Lansing, MI, 48824, United States;Department of Statistics and Probability, Michigan State University, East Lansing, MI, 48824, United States
Venue:
Journal of Multivariate Analysis
Year:
2010

Citing 2
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Halfspace depth and regression depth characterize the empirical distribution

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Second-order accuracy of depth-based bootstrap confidence regions

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Abstract

The Tukey depth is an innovative concept in multivariate data analysis. It can be utilized to extend the univariate order concept and advantages to a multivariate setting. While it is still an open question as to whether the depth contours uniquely determine the underlying distribution, some positive answers have been provided. We extend these results to distributions with smooth depth contours, with elliptically symmetric distributions as special cases. The key ingredient of our proofs is the well-known Cramer-Wold theorem.