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- W2155623416 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." @default.
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- W2155623416 date "2012-01-01" @default.
- W2155623416 modified "2023-10-13" @default.
- W2155623416 title "An Exact Algorithm for Weighted-Mean Trimmed Regions in Any Dimension" @default.
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- W2155623416 doi "https://doi.org/10.18637/jss.v047.i13" @default.
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