Cramér type large deviations for trimmed L-statistics
DOI:
https://doi.org/10.19195/0208-4147.37.1.4Słowa kluczowe:
Trimmed L-statistics, central limit theorem, large deviations, moderate deviationsAbstrakt
CRAMÉR TYPE LARGE DEVIATIONS FOR TRIMMED L-STATISTICS
In this paper, we propose a new approach to the investigationof asymptotic properties of trimmed L-statistics and we apply it to the Cramér 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 onWinsorized random variables. Using this method, we establish the Cramér type large deviation results for the trimmed L-statistics under quite mild and natural conditions.
