自正则部分和精确渐近性的一般结果

华东师范大学学报(自然科学版) ›› 2013, Vol. 2013 ›› Issue (2): 146-153, 159.

自正则部分和精确渐近性的一般结果

陆振刚¹, 姜玉秋²

1. 四平职业大学~~宣传部, 吉林~~四平 136002;
2. 吉林师范大学~~数学学院, 吉林~~四平 136000

收稿日期:2012-04-01 修回日期:2012-07-01 出版日期:2013-03-25 发布日期:2013-03-20

General result on precise asymptotics for self-normalized sums

LU Zhen-gang ¹, JIANG Yu-qiu ²

1. Propaganda Department, Siping Professional College, Siping Jilin 136002, China;
2. College of Mathematics, Jilin Normal University, Siping Jilin 136000, China

Received:2012-04-01 Revised:2012-07-01 Online:2013-03-25 Published:2013-03-20

摘要/Abstract

摘要： 设一零均值非退化、属于正态吸引域的独立同分布随机变量序列,
利用独立序列的弱收敛定理和尾概率不等式, 对于更为广泛的边界函数,
证明了其自正则部分和精确渐近性的一般结果, 揭示了
拟权函数、边界函数、收敛速度和极限值之间的关系,
改进并推广了已有的结果.

关键词: 精确渐近性, 自正则和, 一般结果, 独立同分布

Abstract: Gien a sequence of i.i.d.~nondegenerate random variables
with zero means and belonging to the domain of attraction of the
normal law, by the weak convergence theorem and the tail probability
inequalities of the independent and identically distributed
sequence, a general result on precise asymptotics for the
self-normalized sums with generalized boundary functions has been
proved. It can describe the relations among the weighted function,
boundary function, convergence rate and limit value, then the known
results of this field are improved and extended.

Key words: precise asymptotics, self-normalized sums, a general result, independent and identically distributed (i.i.d.)

中图分类号:

O211.4

陆振刚, 姜玉秋. 自正则部分和精确渐近性的一般结果[J]. 华东师范大学学报(自然科学版), 2013, 2013(2): 146-153, 159.

LU Zhen-gang, JIANG Yu-qiu. General result on precise asymptotics for self-normalized sums[J]. Journal of East China Normal University(Natural Sc, 2013, 2013(2): 146-153, 159.

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