Title: Halfspace Depth and Regression Depth Characterize the Empirical Distribution
Authors: Struyf, Anja ×
Rousseeuw, Peter #
Issue Date: 1999
Publisher: Elsevier
Series Title: Journal of Multivariate Analysis vol:69 issue:1 pages:135-153
Abstract: 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.
ISSN: 0047-259X
Publication status: published
KU Leuven publication type: IT
Appears in Collections:Statistics Section
× corresponding author
# (joint) last author

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