@article{JSSv047i13,
title={An Exact Algorithm for Weighted-Mean Trimmed Regions in Any Dimension},
volume={47},
url={https://www.jstatsoft.org/index.php/jss/article/view/v047i13},
doi={10.18637/jss.v047.i13},
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.},
number={13},
journal={Journal of Statistical Software},
author={Bazovkin, Pavel and Mosler, Karl},
year={2012},
pages={1–29}
}