阵列自正则和的单对数律

doi:10.6040/j.issn.1671-9352.0.2021.447

《山东大学学报(理学版)》 ›› 2021, Vol. 56 ›› Issue (12): 78-83.doi: 10.6040/j.issn.1671-9352.0.2021.447

• • 上一篇

阵列自正则和的单对数律

柯春梅¹,陈亮陆¹,黄颖强^2*

1.暨南大学统计学系, 广东广州 510630;2.广州华商学院数据科学学院, 广东广州 511300

发布日期:2021-11-25
作者简介:柯春梅(1987— ), 女, 硕士, 助教, 研究方向为概率极限理论. E-mail:212618310@qq.com*通信作者简介:黄颖强(1961— ), 男, 副教授, 研究方向为大样本理论及应用. E-mail:acc2009@163.com

Law of the single logarithm for the self-normalized sums for arrays

KE Chun-mei¹, CHEN Liang-lu¹, HUANG Ying-qiang^2*

1. Department of Statistics, Jinan University, Guangzhou 510630, Guangdong, China;
2. School of Data Science, Guangzhou Huashang College, Guangzhou 511300, Guangdong, China

Published:2021-11-25

摘要/Abstract

摘要： 利用随机变量序列自正则和的中偏差理论,研究了随机变量阵列自正则和的单对数律,推广了已有的结果。作为应用,给出了随机变量阵列t-统计量的单对数律。

关键词: 自正则和, 单对数律, 阵列, 中偏差

Abstract: By the self-normalized sum moderate deviations, the law of the single logarithm for the self-normalized sums for arrays is obtained, which generalizes the current results. As the application, the law of the single logarithm for the t-statistics of arrays is derived.

Key words: self-normalized sum, law of the single logarithm, array, moderate deviation

中图分类号:

O211.4

柯春梅,陈亮陆,黄颖强. 阵列自正则和的单对数律[J]. 《山东大学学报(理学版)》, 2021, 56(12): 78-83.

KE Chun-mei, CHEN Liang-lu, HUANG Ying-qiang. Law of the single logarithm for the self-normalized sums for arrays[J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2021, 56(12): 78-83.

参考文献

[1] 林正炎,陆传荣,苏中根. 概率极限理论基础[M]. 北京:高等教育出版社,1999. LIN Zhengyan, LU Chuanrong, SU Zhonggen. Foundations of probability limit theory[M]. Beijing: Higher Education Press, 1999.
[2] LI D L, RAO M B, TOMKINS R J. A strong law for B-valued arrays[J]. Proceedings of the American Mathematical Society, 1995, 123(10):3205-3212.
[3] QI Y C. On the strong convergence of arrays[J]. Bulletin of the Australian Mathematical Society, 1994, 50(2):219-223.
[4] 张国辉, 陈平炎. 阵列的Chung型单对数律[J]. 数学学报, 2017,60(5):883-888. ZHANG Guohui, CHEN Pingyan. Chungs type law of the single logarithm for arrays[J]. Acta Mathematica Sinica, Chinese Series, 2017, 60(5):883-888.
[5] 冯志伟. 阵列的单对数极限律[J]. 山东大学学报(理学版), 2014, 49(7):75-79. FENG Zhiwei. The limit law of the single logarithm for arrays[J]. Journal of Shandong University(Natural Science), 2014, 49(7):75-79.
[6] 刘洋,冯志伟,陈平炎. 随机变量阵列的几乎处处中心极限定理[J]. 山东大学学报(理学版), 2016, 51(6):24-29. LIU Yang, FENG Zhiwei, CHEN Pingyan. Almost sure central limit theorem for arrays of random variables[J]. Journal of Shandong University(Natural Science), 2016, 51(6):24-29.
[7] CHEN P Y, YE X Q, HU T C. A strong law and a law of the single logarithm for arrays of rowwise independent random variables [J]. Statistics & Probability Letters, 2016, 110(3):169-174.
[8] GRIFFIN P, KUELBS J. Self-normalized laws of the iterated logarithm[J]. Annals of Probability, 1989, 17(4):1571-1601.
[9] FELLER W. An introduction to probability theory and its applications(II)[M]. New Deli: John Wiley & Sons, 1965.
[10] SHAO Q M. Self-normalized large deviations[J]. Annals of Probability, 1997, 25(1):285-328.
[11] HARVATH L, SHAO Q M. Large deviations and law of the iterated logarithm for partial sums normalized by the largest absolute observation[J]. Annals of Probability, 1996, 24(3):1368-1387.
[12] KATZ M L. The probability in the tail of a distribution[J]. The Annals of Mathematical Statistics, 1963, 34(1):312-318.

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阵列自正则和的单对数律

Law of the single logarithm for the self-normalized sums for arrays

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