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Discussion Papers in Statistics and Econometrics, Seminar für Wirtschafts- und Sozialstatistik, Universität Köln >
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http://hdl.handle.net/10419/45356
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| Title: | | An exact algorithm for weighted-mean trimmed regions in any dimension  |
| Authors: | | Bazovkin, Pavel Mosler, Karl |
| Issue Date: | | 2010 |
| Series/Report no.: | | Discussion papers in statistics and econometrics 6/10 |
| 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. |
| Subjects: | | central regions data depth multivariate data analysis convex polytope computational geometry algorithm C++, R |
| Document Type: | | Working Paper |
| Appears in Collections: | | Discussion Papers in Statistics and Econometrics, Seminar für Wirtschafts- und Sozialstatistik, Universität Köln
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