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.
Sharp large deviations L-statistics Change of measure method
Mathematics Subject Classification
62N02 60F15 60G50
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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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