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Multivariate order statistics via multivariate concomitants

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  • Arnold, Barry C.
  • Castillo, Enrique
  • Sarabia, Jos Mara

Abstract

Let 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.

Suggested Citation

  • Arnold, Barry C. & Castillo, Enrique & Sarabia, Jos Mara, 2009. "Multivariate order statistics via multivariate concomitants," Journal of Multivariate Analysis, Elsevier, vol. 100(5), pages 946-951, May.
    • Handle: RePEc:eee:jmvana:v:100:y:2009:i:5:p:946-951
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    References listed on IDEAS

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    1. Bairamov, Ismihan, 2006. "Progressive Type II censored order statistics for multivariate observations," Journal of Multivariate Analysis, Elsevier, vol. 97(4), pages 797-809, April.
    2. Kaufmann, E. & Reiss, R. -D., 1992. "On conditional distributions of nearest neighbors," Journal of Multivariate Analysis, Elsevier, vol. 42(1), pages 67-76, July.
    3. Balakrishnan, N., 1993. "Multivariate normal distribution and multivariate order statistics induced by ordering linear combinations," Statistics & Probability Letters, Elsevier, vol. 17(5), pages 343-350, August.
    4. M. Jones, 2004. "Families of distributions arising from distributions of order statistics," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 13(1), pages 1-43, June.
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    Cited by:

    1. Edward W. Sun & Yu-Jen Wang & Min-Teh Yu, 2018. "Integrated Portfolio Risk Measure: Estimation and Asymptotics of Multivariate Geometric Quantiles," Computational Economics, Springer;Society for Computational Economics, vol. 52(2), pages 627-652, August.
    2. Chu, Ba & Huynh, Kim & Jacho-Chavez, David, 2013. "Functionals of order statistics and their multivariate concomitants with application to semiparametric estimation by nearest neighbours," MPRA Paper 79670, University Library of Munich, Germany, revised 2012.

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