Universität zu Köln

Dyckerhoff, Rainer and Mozharovskyi, Pavlo (2016). Exact computation of the halfspace depth. Comput. Stat. Data Anal., 98. S. 19 - 31. AMSTERDAM: ELSEVIER SCIENCE BV. ISSN 1872-7352

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Abstract

For computing the exact value of the halfspace depth of a point w.r.t. a data cloud of n points in arbitrary dimension, a theoretical framework is suggested. Based on this framework a whole class of algorithms can be derived. In all of these algorithms the depth is calculated as the minimum over a finite number of depth values w.r.t. proper projections of the data cloud. Three variants of this class are studied in more detail. All of these algorithms are capable of dealing with data that are not in general position and even with data that contain ties. As is shown by simulations, all proposed algorithms prove to be very efficient. (C) 2015 Elsevier B.V. All rights reserved.

Item Type:	Journal Article
Creators:	Creators Email ORCID ORCID Put Code Dyckerhoff, Rainer UNSPECIFIED UNSPECIFIED UNSPECIFIED Mozharovskyi, Pavlo UNSPECIFIED UNSPECIFIED UNSPECIFIED
URN:	urn:nbn:de:hbz:38-275109
DOI:	10.1016/j.csda.2015.12.011
Journal or Publication Title:	Comput. Stat. Data Anal.
Volume:	98
Page Range:	S. 19 - 31
Date:	2016
Publisher:	ELSEVIER SCIENCE BV
Place of Publication:	AMSTERDAM
ISSN:	1872-7352
Language:	English
Faculty:	Unspecified
Divisions:	Unspecified
Subjects:	no entry
Uncontrolled Keywords:	Keywords Language TUKEY DEPTH; LOCATION DEPTH; CONTOURS; NOTION Multiple languages Computer Science, Interdisciplinary Applications; Statistics & Probability Multiple languages
Refereed:	Yes
URI:	http://kups.ub.uni-koeln.de/id/eprint/27510