Cramér moderate deviations for a supercritical Galton–Watson process

Cramér moderate deviations for a supercritical Galton–Watson process

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 Cramér moderate deviation results for the Lotka–Nagaev estimator via a martingale method. Applications to construction of confidence...

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Veröffentlicht in:Statistics & probability letters 2023-01, Vol.192, p.109711, Article 109711
Hauptverfasser: Doukhan, Paul, Fan, Xiequan, Gao, Zhi-Qiang
Format: Artikel
Sprache:eng
Schlagworte:
Cramér moderate deviations
Lotka–Nagaev estimator
Offspring mean
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Zusammenfassung: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 Cramér moderate deviation results for the Lotka–Nagaev estimator via a martingale method. Applications to construction of confidence intervals are also given.
ISSN:0167-7152
1879-2103
DOI:10.1016/j.spl.2022.109711