Cramér type large deviations for trimmed L-statistics

Probability and Mathematical Statistics. 2017. Vol. 37. No. 1. P. 101–118.

Gribkova N.

In this paper, we propose a new approach to the investigation of 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 on Winsorized random variables. Using this method, we establish the Cramér type large deviation results for the trimmed L-statistics under quite mild and natural conditions.

Ключевые слова: central limit theorem, центральная предельная теорема, large deviations, Большие уклонения, Moderate deviations, Умеренные уклонения, Trimmed L-statistics, Усеченные L-статистики