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Halfspace Depth and Regression Depth Characterize the Empirical Distribution

✍ Scribed by Anja J Struyf; Peter J Rousseeuw

Publisher
Elsevier Science
Year
1999
Tongue
English
Weight
332 KB
Volume
69
Category
Article
ISSN
0047-259X

No coin nor oath required. For personal study only.

✦ Synopsis

For multivariate data, the halfspace depth function can be seen as a natural and affine equivariant generalization of the univariate empirical cdf. For any multivariate data set, we show that the resulting halfspace depth function completely determines the empirical distribution. We do this by actually reconstructing the data points from the depth contours. The data need not be in general position. Moreover, we prove the same property for regression depth.

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