Cramér moderate deviations for a supercritical Galton-Watson process

09/25/2021

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by   Paul Doukhan, et al.

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Let (Z_n)_n≥0 be a supercritical Galton-Watson process. The Lotka-Nagaev estimator Z_n+1/Z_n 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.