Universität zu Köln

Liu, Xiaohui, Mosler, Karl and Mozharovskyi, Pavlo (2019). Fast Computation of Tukey Trimmed Regions and Median in Dimension p > 2. J. Comput. Graph. Stat., 28 (3). S. 682 - 698. ALEXANDRIA: AMER STATISTICAL ASSOC. ISSN 1537-2715

Full text not available from this repository.

Abstract

Given data in , a Tukey kappa-trimmed region is the set of all points that have at least Tukey depth kappa w.r.t. the data. As they are visual, affine equivariant and robust, Tukey regions are useful tools in nonparametric multivariate analysis. While these regions are easily defined and interpreted, their practical use in applications has been impeded so far by the lack of efficient computational procedures in dimension p > 2. We construct two novel algorithms to compute a Tukey kappa-trimmed region, a naive one and a more sophisticated one that is much faster than known algorithms. Further, a strict bound on the number of facets of a Tukey region is derived. In a large simulation study the novel fast algorithm is compared with the naive one, which is slower and by construction exact, yielding in every case the same correct results. Finally, the approach is extended to an algorithm that calculates the innermost Tukey region and its barycenter, the Tukey median. for this article are available online.

Item Type:	Journal Article
Creators:	Creators Email ORCID ORCID Put Code Liu, Xiaohui UNSPECIFIED UNSPECIFIED UNSPECIFIED Mosler, Karl UNSPECIFIED UNSPECIFIED UNSPECIFIED Mozharovskyi, Pavlo UNSPECIFIED UNSPECIFIED UNSPECIFIED
URN:	urn:nbn:de:hbz:38-135502
DOI:	10.1080/10618600.2018.1546595
Journal or Publication Title:	J. Comput. Graph. Stat.
Volume:	28
Number:	3
Page Range:	S. 682 - 698
Date:	2019
Publisher:	AMER STATISTICAL ASSOC
Place of Publication:	ALEXANDRIA
ISSN:	1537-2715
Language:	English
Faculty:	Unspecified
Divisions:	Unspecified
Subjects:	no entry
Uncontrolled Keywords:	Keywords Language REGRESSION DEPTH; LOCATION DEPTH; MULTIVARIATE; CONTOURS Multiple languages Statistics & Probability Multiple languages
Refereed:	Yes
URI:	http://kups.ub.uni-koeln.de/id/eprint/13550