Published by the Foundation for Open Access Statistics Editors-in-chief: Bettina Grün, Torsten Hothorn, Rebecca Killick, Edzer Pebesma, Achim Zeileis    ISSN 1548-7660; CODEN JSSOBK
Authors: Pavel Bazovkin, Karl Mosler
Title: An Exact Algorithm for Weighted-Mean Trimmed Regions in Any Dimension
Abstract: Trimmed regions are a powerful tool of multivariate data analysis. They describe a probability distribution in Euclidean d-space regarding location, dispersion, and shape, and they order multivariate data with respect to their centrality. Dyckerhoff and Mosler (2011) have introduced the class of weighted-mean trimmed regions, which possess attractive properties regarding continuity, subadditivity, and monotonicity. We present an exact algorithm to compute the weighted-mean trimmed regions of a given data cloud in arbitrary dimension d. These trimmed regions are convex polytopes in Rd. To calculate them, the algorithm builds on methods from computational geometry. A characterization of a region’s facets is used, and information about the adjacency of the facets is extracted from the data. A key problem consists in ordering the facets. It is solved by the introduction of a tree-based order, by which the whole surface can be traversed efficiently with the minimal number of computations. The algorithm has been programmed in C++ and is available as the R package WMTregions.

Page views:: 2636. Submitted: 2011-02-24. Published: 2012-05-17.
Paper: An Exact Algorithm for Weighted-Mean Trimmed Regions in Any Dimension     Download PDF (Downloads: 2330)
WMTregions_3.2.5.tar.gz: R source package Download (Downloads: 470; 36KB)
v47i13.R: R example code from the paper Download (Downloads: 515; 361B)
Indices_0809.dat: Supplementary data Download (Downloads: 509; 10KB)

DOI: 10.18637/jss.v047.i13

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Paper: Creative Commons Attribution 3.0 Unported License
Code: GNU General Public License (at least one of version 2 or version 3) or a GPL-compatible license.