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Distribution of extremal order statistics from large subsets of concomitants

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  • Wang, Ke
  • Nagaraja, H.N.

Abstract

From a random sample of size n from an absolutely continuous bivariate population (X,Y) we consider two complementary (upper and lower) subsets of Y-values formed by a sorting on the basis of the corresponding X-values. We derive the finite-sample and asymptotic joint distributions of the extreme order statistics of these Y subsets assuming that the subset sizes remain proportional to n as n-->[infinity]. We illustrate the use of our results with the bivariate normal example and provide an approximation to the probability of an event of interest in selection problems.

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  • Wang, Ke & Nagaraja, H.N., 2010. "Distribution of extremal order statistics from large subsets of concomitants," Statistics & Probability Letters, Elsevier, vol. 80(7-8), pages 534-539, April.
    • Handle: RePEc:eee:stapro:v:80:y:2010:i:7-8:p:534-539
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    References listed on IDEAS

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    1. Kaufmann, E. & Reiss, R. -D., 1992. "On conditional distributions of nearest neighbors," Journal of Multivariate Analysis, Elsevier, vol. 42(1), pages 67-76, July.
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