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arXiv · 2109.12374

Cram\'{e}r moderate deviations for a supercritical Galton-Watson process

Paul Doukhan·Xiequan Fan·Zhi-Qiang Gao
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Abstract

Let $(Z_n)_{n\geq0}$ 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 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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Paul Doukhan, Xiequan Fan, Zhi-Qiang Gao. 2021-09-25. Cram\'{e}r moderate deviations for a supercritical Galton-Watson process. https://arxiv.org/abs/2109.12374

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