Multivariate order statistics via multivariate concomitants

  • Authors:

  • Barry C. Arnold;Enrique Castillo;José María Sarabia

  • Affiliations:

  • Department of Statistics, University of California, Riverside, USA;Department of Applied Mathematics and Computational Sciences, University of Cantabria, Spain and University of Castilla-La Mancha, Spain;Department of Economics, University of Cantabria, Spain

  • Venue:
  • Journal of Multivariate Analysis
  • Year:
  • 2009

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Abstract

Let X@?"1,...,X@?"n denote a set of n independent identically distributed k-dimensional absolutely continuous random variables. A general class of complete orderings of such random vectors is supplied by viewing them as concomitants of an auxiliary random variable. The resulting definitions of multivariate order statistics subsume and extend orderings that have been previously proposed such as norm ordering and N-conditional ordering. Analogous concepts of multivariate record values and multivariate generalized order statistics are also described.