An exact algorithm for weighted-mean trimmed regions in any dimension

Pavel Bazovkin and Karl Mosler

No 6/10, Discussion Papers in Econometrics and Statistics from University of Cologne, Institute of Econometrics and Statistics

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 (201x) 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. The algorithm has been programmed in C++ and is available as an R package.

Keywords: central regions; data depth; multivariate data analysis; convex polytope; computational geometry; algorithm; C++; R (search for similar items in EconPapers)
Date: 2010
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Citations: View citations in EconPapers (4)

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Related works:
Journal Article: An Exact Algorithm for Weighted-Mean Trimmed Regions in Any Dimension (2012)
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