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

Hui Jiang (), Jin Shao () and Qingshan Yang ()
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Hui Jiang: Nanjing University of Aeronautics and Astronautics
Jin Shao: Nanjing University of Aeronautics and Astronautics
Qingshan Yang: Northeast Normal University

Statistical Papers, 2021, vol. 62, issue 2, No 8, 744 pages

Abstract: 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; 62N02; 60F15; 60G50 (search for similar items in EconPapers)
Date: 2021
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DOI: 10.1007/s00362-019-01109-8

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