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Saddlepoint Approximations for the Difference of Order Statistics and Studentized Sample Quantiles

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  • Chunsheng Ma
  • John Robinson

Abstract

For a sample from a given distribution the difference of two order statistics and the Studentized quantile are statistics whose distribution is needed to obtain tests and confidence intervals for quantiles and quantile differences. This paper gives saddlepoint approximations for densities and saddlepoint approximations of the Lugannani–Rice form for tail probabilities of these statistics. The relative errors of the approximations are n−1 uniformly in a neighbourhood of the parameters and this uniformity is global if the densities are log‐concave.

Suggested Citation

  • Chunsheng Ma & John Robinson, 1999. "Saddlepoint Approximations for the Difference of Order Statistics and Studentized Sample Quantiles," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 61(3), pages 563-577.
    • Handle: RePEc:bla:jorssb:v:61:y:1999:i:3:p:563-577
    DOI: 10.1111/1467-9868.00193
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    Cited by:

    1. Dominique Guegan & Bertrand K. Hassani & Kehan Li, 2016. "A robust confidence interval of historical Value-at-Risk for small sample," Documents de travail du Centre d'Economie de la Sorbonne 16034, Université Panthéon-Sorbonne (Paris 1), Centre d'Economie de la Sorbonne.
    2. Arellano-Valle, Reinaldo B. & Genton, Marc G., 2007. "On the exact distribution of linear combinations of order statistics from dependent random variables," Journal of Multivariate Analysis, Elsevier, vol. 98(10), pages 1876-1894, November.
    3. Dominique Guegan & Bertrand Hassani & Kehan Li, 2017. "Measuring risks in the extreme tail: The extreme VaR and its confidence interval," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-01317391, HAL.

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