Cram\'er type large deviations for trimmed L-statistics
Abstract
In this paper, we propose a new approach to the investigation of asymptotic properties of trimmed L-statistics and we apply it to the Cram\'er type large deviation problem. Our results can be compared with ones in Callaert et al.(1982) -- the first and, as far as we know, the single article, where some results on probabilities of large deviations for the trimmed L-statistics were obtained, but under some strict and unnatural conditions. Our approach is to approximate the trimmed L-statistic by a non-trimmed L-statistic (with smooth weight function) based on Winsorized random variables. Using this method, we establish the Cram\'er type large deviation results for the trimmed L-statistics under quite mild and natural conditions.
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