An exact algorithm for weighted-mean trimmed regions in any dimension
AbstractTrimmed 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. --
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Bibliographic InfoPaper provided by University of Cologne, Department for Economic and Social Statistics in its series Discussion Papers in Statistics and Econometrics with number 6/10.
Date of creation: 2010
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central regions; data depth; multivariate data analysis; convex polytope; computational geometry; algorithm; C++; R;
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- Bazovkin, Pavel & Mosler, Karl, 2011. "Stochastic linear programming with a distortion risk constraint," Discussion Papers in Statistics and Econometrics 6/11, University of Cologne, Department for Economic and Social Statistics.
- Wiechers, Christof, 2011. "Construction of uncertainty sets for portfolio selection problems," Discussion Papers in Statistics and Econometrics 4/11, University of Cologne, Department for Economic and Social Statistics.
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