Self-normalized Cramér moderate deviations for a supercritical Galton–Watson process

Let $(Z_n)_{n\geq0}$ be a supercritical Galton–Watson process. Consider the Lotka–Nagaev estimator for the offspring mean. In this paper we establish self-normalized Cramér-type moderate deviations and Berry–Esseen bounds for the Lotka–Nagaev estimator. The results are believed to be optimal or near...

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Bibliographic Details
Published inJournal of applied probability Vol. 60; no. 4; pp. 1281 - 1292
Main Authors Fan, Xiequan, Shao, Qi-Man
Format Journal Article
LanguageEnglish
Published Cambridge, UK Cambridge University Press 01.12.2023
Subjects
Branching (mathematics)
Deviation
Maximum likelihood method
Normal distribution
Original Article
Random variables
Statistical inference
Stochastic processes
Berry–Esseen bounds
60F10
Lotka–Nagaev estimator
60J80
offspring mean
62F12
62F03
Self-normalized processes
Online AccessGet full text
ISSN0021-9002
1475-6072
DOI10.1017/jpr.2022.134

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Summary:Let $(Z_n)_{n\geq0}$ be a supercritical Galton–Watson process. Consider the Lotka–Nagaev estimator for the offspring mean. In this paper we establish self-normalized Cramér-type moderate deviations and Berry–Esseen bounds for the Lotka–Nagaev estimator. The results are believed to be optimal or near-optimal.
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ISSN:0021-9002
1475-6072
DOI:10.1017/jpr.2022.134