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

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Xiequan Fan, Qi-Man Shao

Published: 01 Jan 2023, Last Modified: 16 May 2025J. Appl. Probab. 2023EveryoneRevisionsBibTeXCC BY-SA 4.0
Abstract: 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.