Smooth depth contours characterize the underlying distribution

Linglong Kong and Yijun Zuo

Journal of Multivariate Analysis, 2010, vol. 101, issue 9, 2222-2226

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 Cramér-Wold theorem.

Keywords: Halfspace; depth; Depth; contour; Characterization; Smooth; contour (search for similar items in EconPapers)
Date: 2010
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Citations: View citations in EconPapers (9)

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