EconPapers    
Economics at your fingertips  
 

Halfspace Depth and Regression Depth Characterize the Empirical Distribution

Anja J. Struyf and Peter Rousseeuw ()

Journal of Multivariate Analysis, 1999, vol. 69, issue 1, 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.

Keywords: location depth; multivariate ranking; reconstruction algorithm; regression depth (search for similar items in EconPapers)
Date: 1999
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (18) Track citations by RSS feed

Downloads: (external link)
http://www.sciencedirect.com/science/article/pii/S0047-259X(98)91804-8
Full text for ScienceDirect subscribers only

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:eee:jmvana:v:69:y:1999:i:1:p:135-153

Ordering information: This journal article can be ordered from
http://www.elsevier.com/wps/find/supportfaq.cws_home/regional
https://shop.elsevie ... _01_ooc_1&version=01

Access Statistics for this article

Journal of Multivariate Analysis is currently edited by de Leeuw, J.

More articles in Journal of Multivariate Analysis from Elsevier
Bibliographic data for series maintained by Haili He ().

 
Page updated 2020-09-12
Handle: RePEc:eee:jmvana:v:69:y:1999:i:1:p:135-153