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Data Depth and Maximum Feasible Subsystems

In: Graph Theory and Combinatorial Optimization

Author

Listed:
  • Komei Fukuda
  • Vera Rosta

Abstract

Various data depth measures were introduced in nonparametric statistics as multidimensional generalizations of ranks and of the median. A related problem in optimization is to find a maximum feasible subsystem, that is a solution satisfying as many constrainsts as possible, in a given system of linear inequalities. In this paper we give a unified framework for the main data depth measures such as the halfspace depth, the regression depth and the simplicial depth, and we survey the related results from nonparametric statistics, computational geometry, discrete geometry and linear optimization.

Suggested Citation

  • Komei Fukuda & Vera Rosta, 2005. "Data Depth and Maximum Feasible Subsystems," Springer Books, in: David Avis & Alain Hertz & Odile Marcotte (ed.), Graph Theory and Combinatorial Optimization, chapter 0, pages 37-67, Springer.
    • Handle: RePEc:spr:sprchp:978-0-387-25592-7_3
    DOI: 10.1007/0-387-25592-3_3
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    Cited by:

    1. Marc Hallin & Davy Paindaveine & Miroslav Siman, 2008. "Multivariate quantiles and multiple-output regression quantiles: from L1 optimization to halfspace depth," Working Papers ECARES 2008_042, ULB -- Universite Libre de Bruxelles.
    2. Paindaveine, Davy & Siman, Miroslav, 2011. "On directional multiple-output quantile regression," Journal of Multivariate Analysis, Elsevier, vol. 102(2), pages 193-212, February.

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