Self-normalized Cramér type moderate deviations for martingales and applications

被引：0

作者：

Fan, Xiequan ^{[1
]}

Shao, Qi-man ^{[2
]}

机构：

[1] Northeastern Univ Qinhuangdao, Sch Math & Stat, Qinhuangdao, Peoples R China

[2] Southern Univ Sci & Technol, Natl Ctr Appl Math Shenzhen, Dept Stat & Data Sci, SICM, Shenzhen 518000, Peoples R China

来源：

BERNOULLI | 2025年 / 31卷 / 01期

基金：

中国国家自然科学基金;

关键词：

Branching process in a random environment; Cram & eacute; r's moderate deviations; martingales; self-normalized sequences; Student's statistic; SUBCRITICAL BRANCHING-PROCESSES; RANDOM ENVIRONMENT; LIMIT-THEOREMS; STATIONARY-SEQUENCES; MOMENTS;

D O I：

10.3150/24-BEJ1722

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：

Cram & eacute;r's moderate deviations give a quantitative estimate for the relative error of the normal approximation and provide theoretical justifications for many estimators used in statistics. In this paper, we establish self-normalized Cram & eacute;r type moderate deviations for martingales under some mild conditions. The result extends an earlier work of Fan et al. (Bernoulli 25 (2019) 2793-2823). Moreover, applications of our result to Student's statistic, stationary martingale difference sequences and branching processes in a random environment are also discussed.

引用

页码：130 / 161

页数：32

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