Cramér moderate deviations for a supercritical Galton–Watson process

Statistics & Probability Letters（2023）

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摘要

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.

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