DOI

In this article, we establish
Cram\'{e}r type moderate deviation results for (intermediate) trimmed means
$T_n=n^{-1} \sum_{i=\kn+1}^{n-\mn}\xin$, where $\xin$ -- the order statistics corresponding to the first $n$
observations
in a~sequence $X_1,X_2,\dots $ of i.i.d random variables with $df$ $F$.
We consider two cases of intermediate and heavy trimming. In the former case, when $\max(\an,\bn)\to 0$ ($\an=\kn/n$, $\bn=\mn/n$) and $\min(\kn,\mn)\to\infty$ as $\nty$, we
obtain our results under a~natural moment assumption and a~mild condition on the rate at which $\an$ and $\bn$ 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 an~open set containing the limit points of the trimming sequences $\an$, $1-\bn$.
Язык оригиналаанглийский
Страницы (с-по)11918-11932
Число страниц15
ЖурналCommunications in Statistics - Theory and Methods
Том46
Номер выпуска23
DOI
СостояниеОпубликовано - 1 мар 2017

    Области исследований

  • intermediate trimmed means, moderate deviations, large deviations, slightly trimmed sums, asymptotic normality

    Предметные области Scopus

  • Математика (все)

ID: 9216185