Self-normalized moderate random deviations for independent variables

Let X1,X2,... be a sequence of independent random variables （r.v.s） belonging to the domain of attraction of a normal or stable law. In this paper, we study moderate deviations for the self-normalized sum n X ∑^n_i=1Xi/Vm,p ,where Vn,p （∑^n_i=1｜Xi｜p）^1/p （P 〉 1）.Applications to the self-normalized l...

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Bibliographic Details
Published in中国科学：数学英文版 Vol. 55; no. 11; pp. 2297 - 2315
Main Author JING BingYi LIANG HanYing ZHOU Wang
Format Journal Article
LanguageEnglish
Published 2012
Subjects
加权求和
吸引域
归一化法
标准化
独立变量
部分和增量
随机偏差
随机变量序列
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Summary:Let X1,X2,... be a sequence of independent random variables （r.v.s） belonging to the domain of attraction of a normal or stable law. In this paper, we study moderate deviations for the self-normalized sum n X ∑^n_i=1Xi/Vm,p ,where Vn,p （∑^n_i=1｜Xi｜p）^1/p （P 〉 1）.Applications to the self-normalized law of the iteratedlogarithm, Studentized increments of partial sums, t-statistic, and weighted sum of independent and identically distributed （i.i.d.） r.v.s are considered.
Bibliography:Let X1,X2,... be a sequence of independent random variables （r.v.s） belonging to the domain of attraction of a normal or stable law. In this paper, we study moderate deviations for the self-normalized sum n X ∑^n_i=1Xi/Vm,p ,where Vn,p （∑^n_i=1｜Xi｜p）^1/p （P 〉 1）.Applications to the self-normalized law of the iteratedlogarithm, Studentized increments of partial sums, t-statistic, and weighted sum of independent and identically distributed （i.i.d.） r.v.s are considered.
self-normalized sum, moderate deviation, t-statistic, LIL, increment
11-1787/N
ISSN:1674-7283
1869-1862