Precise asymptotics in the law of the logarithm for the rescaled range statistic

被引：0

作者：

Pang, Tian-Xiao ^{[1
]}

Lin, Zheng-Yan ^{[1
]}

Hwang, Kyo-Shin ^{[1
]}

机构：

[1] Zhejiang Univ, Dept Math, Hangzhou 310027, Zhejiang, Peoples R China

来源：

JOURNAL OF THE KOREAN STATISTICAL SOCIETY | 2013年 / 42卷 / 02期

基金：

中国国家自然科学基金;

关键词：

Precise asymptotics; Rescaled range statistic; Law of the logarithm; Domain of attraction of the normal law; Complete convergence; A.s; convergence; R/S STATISTICS; ITERATED LOGARITHM; LARGE NUMBERS; RATES;

D O I：

10.1016/j.jkss.2012.07.003

中图分类号：

O21 [概率论与数理统计]; C8 [统计学];

学科分类号：

020208 ; 070103 ; 0714 ;

摘要：

For a sequence of i.i.d. zero mean random variables belonging to the domain of attraction of the normal law, two results concerning the rescaled range statistic are investigated in this paper. More specifically, we obtain precise asymptotics in the law of the logarithm related to complete convergence and a.s. convergence under some mild conditions. (C) 2012 The Korean Statistical Society. Published by Elsevier B.V. All rights reserved.

引用

页码：177 / 189

页数：13

共 50 条

[21] The law of iterated logarithm of rescaled range statistics for AR(1) model
Lin, ZY
Lee, SC
ACTA MATHEMATICA SINICA-ENGLISH SERIES, 2006, 22 (02) : 535 - 544
[22] Precise asymptotics in the law of the iterated logarithm of moving-average processes
Li, YX
Zhang, LX
ACTA MATHEMATICA SINICA-ENGLISH SERIES, 2006, 22 (01) : 143 - 156
[23] Note on Precise Asymptotics in the Law of the Iterated Logarithm under Sublinear Expectations
Xu, Mingzhou
Cheng, Kun
MATHEMATICAL PROBLEMS IN ENGINEERING, 2022, 2022
[24] Precise Asymptotics in the Law of the Iterated Logarithm of Moving-Average Processes
Yun Xia Li
Li Xin Zhang
Acta Mathematica Sinica, 2006, 22 : 143 - 156
[25] The Hurst phenomenon and the rescaled range statistic
Mason, David M.
STOCHASTIC PROCESSES AND THEIR APPLICATIONS, 2016, 126 (12) : 3790 - 3807
[26] ASYMPTOTICS IN THE LAW OF THE ITERATED LOGARITHM
Cwiklinska, M. B.
THEORY OF PROBABILITY AND ITS APPLICATIONS, 2009, 53 (04) : 707 - U143
[27] Precise Asymptotics in the Law of Iterated Logarithm for Moving Average Process under Dependence
Li, Jie
JOURNAL OF INEQUALITIES AND APPLICATIONS, 2011,
[28] A SUPPLEMENT TO PRECISE ASYMPTOTICS IN THE LAW OF THE ITERATED LOGARITHM FOR SELF-NORMALIZED SUMS
Hwang, Kyo-Shin
JOURNAL OF THE KOREAN MATHEMATICAL SOCIETY, 2008, 45 (06) : 1601 - 1611
[29] Precise asymptotics in the law of the iterated logarithm and the complete convergence for uniform empirical process
Zhang, Yong
Yang, Xiao-Yun
STATISTICS & PROBABILITY LETTERS, 2008, 78 (09) : 1051 - 1055
[30] Precise Asymptotics in the Law of Iterated Logarithm for Moving Average Process under Dependence
Jie Li
Journal of Inequalities and Applications, 2011

← 1 2 3 4 5 →