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On stochastic orders of absolute value of order statistics in symmetric distributions

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  • Malinovsky, Yaakov
  • Rinott, Yosef

Abstract

Let Y1,...,Yn be the order statistics of a simple random sample from a finite or infinite population, having median =M. We compare the variables Yj-M and Ym-M, where Ym is the sample median, that is, for odd n. The comparison is in terms of the likelihood ratio order, which implies stochastic order as well as other orders. The results were motivated by the study of best invariant and minimax estimators for the k/N quantile of a finite population of size N, with a natural loss function of the type , where FN is the population distribution function, t is an estimate, and g is an increasing function.

Suggested Citation

  • Malinovsky, Yaakov & Rinott, Yosef, 2009. "On stochastic orders of absolute value of order statistics in symmetric distributions," Statistics & Probability Letters, Elsevier, vol. 79(19), pages 2086-2091, October.
    • Handle: RePEc:eee:stapro:v:79:y:2009:i:19:p:2086-2091
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    References listed on IDEAS

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    1. Colangelo, Antonio & Scarsini, Marco & Shaked, Moshe, 2006. "Some positive dependence stochastic orders," Journal of Multivariate Analysis, Elsevier, vol. 97(1), pages 46-78, January.
    2. Zielinski, Ryszard, 1999. "Best equivariant nonparametric estimator of a quantile," Statistics & Probability Letters, Elsevier, vol. 45(1), pages 79-84, October.
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