Self-normalized Cramér moderate deviations for a supercritical Galton–Watson process

Pub Date : 2023-04-24 DOI:10.1017/jpr.2022.134
Xiequan Fan, Qi-Man Shao
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引用次数: 1

Abstract

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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超临界高尔顿-沃森过程的自归一化cram中度偏差
设$(Z_n)_{n\geq0}$为超临界高尔顿-沃森过程。考虑后代均值的Lotka-Nagaev估计量。本文建立了Lotka-Nagaev估计量的自归一化cram中度偏差和Berry-Esseen界。结果被认为是最优或接近最优的。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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