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Cramér moderate deviations for a supercritical Galton-Watson process

Abstract

Let (Zn)n0(Z_n)_{n\geq0} be a supercritical Galton-Watson process. The Lotka-Nagaev estimator Zn+1/ZnZ_{n+1}/Z_n is a common estimator for the offspring mean.In this paper, we establish some Cram\'{e}r 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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