TY - JOUR

T1 - Cramér-type moderate deviations for intermediate trimmed means

AU - Грибкова, Надежда Викторовна

N1 - Gribkova, N. Cramér-type moderate deviations for intermediate trimmed means. Communications in statistics – Theory and Methods. Vol. 46, 2017, issue 23, Pages: 11918-11932

PY - 2017/3/1

Y1 - 2017/3/1

N2 - In this article, we establishCram\'{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 $n$observationsin 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 $\nty$, weobtain 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 $\an$, $1-\bn$.

AB - In this article, we establishCram\'{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 $n$observationsin 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 $\nty$, weobtain 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 $\an$, $1-\bn$.

KW - intermediate trimmed means

KW - moderate deviations

KW - large deviations

KW - slightly trimmed sums

KW - asymptotic normality

U2 - 10.1080/03610926.2017.1285930

DO - 10.1080/03610926.2017.1285930

M3 - Article

VL - 46

SP - 11918

EP - 11932

JO - Communications in Statistics - Theory and Methods

JF - Communications in Statistics - Theory and Methods

SN - 0361-0926

IS - 23

ER -