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Computing zonoid trimmed regions of dimension d>2

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  • Mosler, Karl
  • Lange, Tatjana
  • Bazovkin, Pavel

Abstract

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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Bibliographic Info

Article provided by Elsevier in its journal Computational Statistics & Data Analysis.

Volume (Year): 53 (2009)
Issue (Month): 7 (May)
Pages: 2500-2510

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Handle: RePEc:eee:csdana:v:53:y:2009:i:7:p:2500-2510

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Web page: http://www.elsevier.com/locate/csda

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Cited by:
  1. 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.
  2. Chiara GIGLIARANO & Karl MOSLER, 2009. "Measuring middle-class decline in one and many attributes," Working Papers 333, Universita' Politecnica delle Marche (I), Dipartimento di Scienze Economiche e Sociali.

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