Cram\'er type moderate deviations for trimmed L-statistics

TL;DR

This paper derives Cramér type moderate deviation results for heavy trimmed L-statistics under mild smoothness conditions, extending previous large deviation work and providing new probabilistic bounds.

Contribution

It introduces moderate deviation results for trimmed L-statistics with minimal smoothness assumptions on the distribution and weights, complementing existing large deviation findings.

Findings

Established Cramér type moderate deviation results for heavy trimmed L-statistics.

Results require only mild smoothness conditions near trimming points.

Extends the theoretical understanding of tail probabilities for L-statistics.

Abstract

We establish Cram\'er type moderate deviation (MD}) 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 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 Cram\'er type large deviations (LD) for trimmed L-statistics by Gribkova (2016) and Callaert et al. (1982).