Large deviations and law of the iterated logarithm for partial sums normalized by the largest absolute observation
成果类型：
Article
署名作者：
Horvath, L; Shao, QM
署名单位：
National University of Singapore
刊物名称：
ANNALS OF PROBABILITY
ISSN/ISSBN：
0091-1798
发表日期：
1996
页码：
1368-1387
关键词：
摘要：
Let {X(n), 1 less than or equal to n < infinity} be a sequence of independent identically distributed random variables in the domain of attraction of a stable law with index 0 < alpha < 2. The limit of x(n)(-1) log P{S-n/max \X(i)\ greater than or equal to x(n)} is found when x(n) --> infinity and x(n)/n --> 0. The large deviation result is used to prove the law of the iterated logarithm for the self-normalized partial sums.