Cramer moderate deviations for a supercritical Galton-Watson process

被引：1
|
作者：
Doukhan, Paul [1 ]
Fan, Xiequan [2 ]
Gao, Zhi-Qiang [3 ]
机构：
[1] CY Univ, AGM, UMR 8088, Site St Martin, F-95000 Cergy Pontoise, France
[2] Tianjin Univ, Ctr Appl Math, Tianjin 300072, Peoples R China
[3] Beijing Normal Univ, Sch Math Sci, Lab Math & Complex Syst, Minist Educ, Beijing 100875, Peoples R China
来源：
STATISTICS & PROBABILITY LETTERS | 2023年 / 192卷
基金：
中国国家自然科学基金;
关键词：
Cram?r moderate deviations; Lotka-Nagaev estimator; Offspring mean; BRANCHING-PROCESS; SUMS; RATES; MOMENTS;
D O I：
10.1016/j.spl.2022.109711
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：
Let (Zn)n >= 0 be a supercritical Galton-Watson process. The Lotka-Nagaev estimator Zn+1/Zn is a common estimator for the offspring mean. In this paper, we establish some Cramer moderate deviation results for the Lotka-Nagaev estimator via a martingale method. Applications to construction of confidence intervals are also given.(c) 2022 Elsevier B.V. All rights reserved.
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页数：10
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