Halfspace Depth and Regression Depth Characterize the Empirical Distribution

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.

MoreLess

Year of publication:	1999
Authors:	Struyf, Anja J. ; Rousseeuw, Peter J.
Published in:	Journal of Multivariate Analysis. - Elsevier, ISSN 0047-259X. - Vol. 69.1999, 1, p. 135-153
Publisher:	Elsevier
Subject:	location depth \| multivariate ranking \| reconstruction algorithm \| regression depth

Online Resource

Check full text access |

More access options

Check Google Scholar

In libraries world-wide (WorldCat)

In German libraries (KVK)

subito order

I need help

More details

Type of publication:	Article
Source:	RePEc - Research Papers in Economics

Persistent link: https://www.econbiz.de/10005152998