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

Published 16 Jul 2021 in math.PR and stat.AP | (2107.07965v1)

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 Cram\'{e}r type moderate deviations and Berry-Esseen's bounds for the Lotka-Nagaev estimator. The results are believed to be optimal or near optimal.

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