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.

引用

页数：10

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