Cramer-type moderate deviations for intermediate trimmed means

摘要

In this article, we establish Cramer-type moderate deviation results for (intermediate) trimmed means T-n = n(- 1)Sigma(n - m)(ni = kn) + 1X(i: n), where X-i: n's are the order statistics corresponding to the first n observations in asequence X-1, X-2, ... of independent identically distributed random variables with F. We consider two cases of intermediate and heavy trimming. In the former case, when max((n), (n)) 0 ((n) = k(n), (n) = m(n)) and min(k(n), m(n)) as n , we obtain our results under anatural moment assumption and amild condition on the rate at which (n) and (n) tend to zero. In the latter case, we do not impose any moment conditions on F, instead, we require some smoothness of F- 1 in anopen set containing the limit points of the trimming sequences alpha(n), 1-beta(n).