Cramér-type moderate deviations for intermediate trimmed means

• DOI: 10.1080/03610926.2017.1285930
• Publication Date: 2017-02-01T14:58:38Z
• Authors: Nadezhda Gribkova
• Keywords: Trimming; Smoothness; Zero (linguistics); Sequence (biology)

In this article, we establish Cramér-type moderate deviation results for (intermediate) trimmed means Tn = n− 1∑n − mni kn + 1Xi: n, where Xi: n's are the order statistics corresponding to first n observations in a sequence X1, X2, … of independent identically distributed random variables with F. We consider two cases intermediate and heavy trimming. former case, when max (αn, βn) → 0 (αn kn/n, βn mn/n) min (kn, mn) ∞ as ∞, obtain our under natural moment assumption mild condition on rate at which αn tend zero. latter do not impose any conditions F, instead, require some smoothness F− 1 an open set containing limit points trimming sequences αn, βn.