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

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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.

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Acknowledgements

The authors would like to express great gratitude to the two anonymous reviewers and the associate editor for the careful reading and constructive comments which led to an improved presentation of this paper.

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Authors and Affiliations

  1. Department of Mathematics, Nanjing University of Aeronautics and Astronautics, Nanjing, 211106, People’s Republic of China

    Hui Jiang & Jin Shao

  2. School of Mathematics and Statistics, Northeast Normal University, Changchun, 130024, People’s Republic of China

    Qingshan Yang

Authors
  1. Hui Jiang
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  2. Jin Shao
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  3. Qingshan Yang
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Correspondence to Qingshan Yang.

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Hui Jiang is supported by National Natural Science Foundation of China(Grant No. 11771209). Jin Shao is supported by the Foundation of Graduate Innovation Center in NUAA (Grant No. KFJJ20170805). Qingshan Yang is supported by National Natural Science Foundation of China (Grant No. 11401090) and the Fundamental Research Funds for the Central University (2412019FZ031).

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Jiang, H., Shao, J. & Yang, Q. Sharp large deviations for a class of normalized L-statistics and applications. Stat Papers 62, 721–744 (2021). https://doi.org/10.1007/s00362-019-01109-8

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  • DOI: https://doi.org/10.1007/s00362-019-01109-8

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