CRAMER TYPE LARGE DEVIATIONS FOR TRIMMED L-STATISTICS

In this paper, we propose a new approach to the investigation of asymptotic properties of trimmed L-statistics and we apply it to the Cramer type large deviation problem. Our results can be compared with those 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 Cramer type large deviation results for the trimmed L-statistics under quite mild and natural conditions.