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

  • Hui Jiang
  • Jin Shao
  • Qingshan YangEmail author
Regular Article
  • 7 Downloads

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.

Keywords

Sharp large deviations L-statistics Change of measure method 

Mathematics Subject Classification

62N02 60F15 60G50 

Notes

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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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Department of MathematicsNanjing University of Aeronautics and AstronauticsNanjingPeople’s Republic of China
  2. 2.School of Mathematics and StatisticsNortheast Normal UniversityChangchunPeople’s Republic of China

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