A strong approximation of self-normalized sums

被引：0

作者：

CSRG Miklós ^{[1
]}

HU ZhiShui ^{[2
]}

机构：

[1] School of Mathematics and Statistics,Carleton University

[2] Department of Statistics and Finance,School of Management,University of Science and Technology of China

来源：

ScienceChina(Mathematics) | 2013年 / 56卷 / 01期

基金：

中央高校基本科研业务费专项资金资助; 加拿大自然科学与工程研究理事会; 中国国家自然科学基金; 高等学校博士学科点专项科研基金;

关键词：

strong approximation; self-normalized sums; domain of attraction of the normal law;

D O I：

暂无

中图分类号：

O211.5 [随机变量];

学科分类号：

020208 ; 070103 ; 0714 ;

摘要：

Let {X,Xn,n1} be a sequence of independent identically distributed random variables with EX=0 and assume that EX2I(|X|≤x) is slowly varying as x→∞,i.e.,X is in the domain of attraction of the normal law.In this paper a Strassen-type strong approximation is established for self-normalized sums of such random variables.

引用

页码：149 / 160

页数：12

共 7 条

[1] Studentized Increments of Partial Sums[J]. Csrg Miklos,林正炎,邵启满.Science in China,Ser.A. 1994(03)
[2] Towards a universal self-normalized moderate deviation
Jing, Bing-Yi
Shao, Qi-Man
Zhou, Wang
[J]. TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 2008, 360 (08) : 4263 - 4285
[3] Self-normalized large deviations
Shao, QM
[J]. ANNALS OF PROBABILITY, 1997, 25 (01) : 285 - 328
[4] REGULARLY VARYING SEQUENCES
GALAMBOS, J
SENETA, E
[J]. PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 1973, 41 (01) : 110 - 116
[5] A converse to the law of the iterated logarithm[J] . V. Strassen.Zeitschrift für Wahrscheinlichkeitstheorie und Verwandte Gebiete . 1966 (4)
[6] An invariance principle for the law of the iterated logarithm[J] . V. Strassen.Zeitschrift für Wahrscheinlichkeitstheorie und Verwandte Gebiete . 1964 (3)
[7] A LIMIT THEOREM FOR THE MAXIMUM OF NORMALIZED SUMS OF INDEPENDENT RANDOM VARIABLES
DARLING, DA
ERDOS, P
[J]. DUKE MATHEMATICAL JOURNAL, 1956, 23 (01) : 143 - 155

← 1 →