English

Self-normalized Cramer moderate deviations for a supercritical Galton-Watson process

Probability 2023-10-03 v1 Applications

Abstract

Let (Zn)n0(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 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}
}
R2 v1 2026-06-24T04:16:07.041Z