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

07/16/2021

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by   Xiequan Fan, et al.

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Let (Z_n)_n≥0 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's bounds for the Lotka-Nagaev estimator. The results are believed to be optimal or near optimal.