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Self-normalized Cramér moderate deviations for a supercritical Galton–Watson process
Published online by Cambridge University Press: 24 April 2023
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.
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- © The Author(s), 2023. Published by Cambridge University Press on behalf of Applied Probability Trust
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