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
收藏
页码：130 / 161
页数：32
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