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Sharp large deviations for a class of normalized L-statistics and applications

Author

Listed:
  • Hui Jiang

    (Nanjing University of Aeronautics and Astronautics)

  • Jin Shao

    (Nanjing University of Aeronautics and Astronautics)

  • Qingshan Yang

    (Northeast Normal University)

Abstract

In this paper, we concentrate on the asymptotic expansion for a class of normalized L-statistics. By the change of measure method, the moment generating function for the combination related to the L-statistics can be estimated explicitly. Then, using asymptotic analysis techniques, we can obtain the sharp large deviations for the above mentioned L-statistics. Finally, our results could be applied to Gini, Fortiana-Grané and Jackson statistics. From the simulation study, we can see that the approximations obtained from the obtained sharp large deviations are very accurate for small tail probabilities.

Suggested Citation

  • Hui Jiang & Jin Shao & Qingshan Yang, 2021. "Sharp large deviations for a class of normalized L-statistics and applications," Statistical Papers, Springer, vol. 62(2), pages 721-744, April.
    • Handle: RePEc:spr:stpapr:v:62:y:2021:i:2:d:10.1007_s00362-019-01109-8
    DOI: 10.1007/s00362-019-01109-8
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    References listed on IDEAS

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    1. Andrius Čiginas, 2014. "On the asymptotic normality of finite population $$L$$ L -statistics," Statistical Papers, Springer, vol. 55(4), pages 1047-1058, November.
    2. Ayyub Sheikhi & Yaser Mehrali & Mahbanoo Tata, 2013. "On the exact joint distribution of a linear combination of order statistics and their concomitants in an exchangeable multivariate normal distribution," Statistical Papers, Springer, vol. 54(2), pages 325-332, May.
    3. Aurea Grané & Josep Fortiana, 2011. "A directional test of exponentiality based on maximum correlations," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 73(2), pages 255-274, March.
    4. Cyrille Joutard, 2017. "Multidimensional strong large deviation results," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 80(6), pages 663-683, November.
    5. Nenghui Kuang & Huantian Xie, 2013. "Large and moderate deviations in testing Rayleigh diffusion model," Statistical Papers, Springer, vol. 54(3), pages 591-603, August.
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