Influence Function of Halfspace Depth

Mario Romanazzi

Journal of Multivariate Analysis, 2001, vol. 77, issue 1, 138-161

Abstract: The sensitivity of halfspace depth values and contours to perturbations of the underlying distribution is investigated. The influence function of the halfspace depth of any point x[set membership, variant]p is bounded and discontinuous; it is constant and positive when the perturbing observation z is placed in any optimal halfspace and it is constant and negative when z is placed in any non-optimal halfspace. When the optimal halfspace is unique a von Mises expansion allows an easy derivation of the asymptotic distribution of the sample halfspace depth. In the sampling case, in general, addition of a single observation outside the convex hull of the sample alters all the depth regions but only the outer region can be arbitrarily expanded. To obtain the same effect on the inner regions the size of the perturbation is required to be not less than the depth orders. Numerical illustrations of the results are given.

Keywords: halfspace; depth; halfspace; region; influence; function; simplicial; depth (search for similar items in EconPapers)
Date: 2001
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (5)

Downloads: (external link)
http://www.sciencedirect.com/science/article/pii/S0047-259X(00)91929-8
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:77:y:2001:i:1:p:138-161

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 Catherine Liu ().