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Asymptotic approximation for the probability density function of an arbitrary sequence of random variables

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  • Joutard, Cyrille

Abstract

We establish a large deviation approximation for the density function of an arbitrary sequence of random variables. The results are analogous to those obtained by Chaganty and Sethuraman (1985). We apply our theorems to the sample variance and the Mann–Whitney two-sample statistic.

Suggested Citation

  • Joutard, Cyrille, 2014. "Asymptotic approximation for the probability density function of an arbitrary sequence of random variables," Statistics & Probability Letters, Elsevier, vol. 90(C), pages 100-107.
    • Handle: RePEc:eee:stapro:v:90:y:2014:i:c:p:100-107
    DOI: 10.1016/j.spl.2014.03.018
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    References listed on IDEAS

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    1. Cyrille Joutard, 2013. "Large deviation approximations for the Mann-Whitney statistic and the Jonckheere-Terpstra statistic," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 25(4), pages 873-888, December.
    2. Cyrille Joutard, 2013. "Strong large deviations for arbitrary sequences of random variables," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 65(1), pages 49-67, February.
    3. Jin, Rungao & Robinson, John, 1999. "Saddlepoint approximation near the endpoints of the support," Statistics & Probability Letters, Elsevier, vol. 45(4), pages 295-303, December.
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