Cramér type moderate deviations for trimmed L-statistics

Abstract

We establish Cramér type moderate deviation results for heavy trimmed L-statistics; we obtain our results under a very mild smoothness condition on the inversion F⁻¹ (F is the underlying distribution function of i.i.d. observations) near two points, where trimming occurs, we assume also some smoothness of weights of the L-statistic. Our results complement previous work on Cramér type large deviations for trimmed L-statistics [8] and [5].