Computing zonoid trimmed regions of dimension d>2
A probability distribution on Euclidean d-space can be described by its zonoid regions. These regions form a nested family of convex sets around the expectation, each being closed and bounded. The zonoid regions of an empirical distribution introduce an ordering of the data that has many applications in multivariate statistical analysis, e.g.cluster analysis, tests for multivariate location and scale, and risk analysis. An exact algorithm is developed to constructing the zonoid regions of a d-variate empirical distribution by their facets when d>=3. The vertices of the region and their adjacency are characterized, and a procedure is suggested by which all vertices and facets can be determined. The algorithm is available as an R-package.
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- Ruts, Ida & Rousseeuw, Peter J., 1996. "Computing depth contours of bivariate point clouds," Computational Statistics & Data Analysis, Elsevier, vol. 23(1), pages 153-168, November.
- Lopez-Pintado, Sara & Romo, Juan, 2007. "Depth-based inference for functional data," Computational Statistics & Data Analysis, Elsevier, vol. 51(10), pages 4957-4968, June.
- Gleb A. Koshevoy & Karl Mosler, 2007. "Multivariate Lorenz dominance based on zonoids," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 91(1), pages 57-76, March.
- Ignacio Cascos & Ilya Molchanov, 2007. "Multivariate risks and depth-trimmed regions," Finance and Stochastics, Springer, vol. 11(3), pages 373-397, July.
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