We establish Cram\'{e}r type moderate deviation ({\it 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\'{e}r type large deviations ({\it LD}) for trimmed $L$-statistics
by Gribkova~(2016) and Callaert et~al.~(1982)
Original languageEnglish
Pages (from-to)313--322
Number of pages15
JournalMathematical Methods of Statistics
Volume25
Issue number4
DOIs
StatePublished - 1 Nov 2016

    Scopus subject areas

  • Mathematics(all)

    Research areas

  • moderate deviations, large deviations, trimmed L-statistics

ID: 9215063