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Bazovkin, Pavel
Mosler, Karl
Year of Publication: 
Series/Report no.: 
Discussion papers in statistics and econometrics 6/10
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.
central regions
data depth
multivariate data analysis
convex polytope
computational geometry
C++, R
Document Type: 
Working Paper

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