Self-normalized Cramer moderate deviations for a supercritical Galton-Watson process
Probability
2023-10-03 v1 Applications
Abstract
Let be a supercritical Galton-Watson process. Consider the Lotka-Nagaev estimator for the offspring mean. In this paper, we establish self-normalized Cram\'{e}r type moderate deviations and Berry-Esseen's bounds for the Lotka-Nagaev estimator. The results are believed to be optimal or near optimal.
Cite
@article{arxiv.2107.07965,
title = {Self-normalized Cramer moderate deviations for a supercritical Galton-Watson process},
author = {Xiequan Fan and Qi-Man Shao},
journal= {arXiv preprint arXiv:2107.07965},
year = {2023}
}