Self-normalized Cram\'{e}r moderate deviations for a supercritical Galton-Watson process
报告题目(Title)：Self-normalized Cram\'{e}r moderate deviations for a supercritical Galton-Watson process
报告人(Speaker)：范协铨副教授 （天津大学）
地点(Place)：教八楼 203 / 腾讯会议 ID：405 784 434
时间(Time)：2021 年 11 月 03 日（周三） 10:00--12:00
邀请人(Inviter)：高志强
报告摘要
Let $(Z_n)_{n \geq 0}$ be a supercritical Galton-Watson process. Consider the Lotka-Nagaev estimator for the offspring mean. In this paper, we establish self-normalized Cramer type moderate deviations and Berry-Esseen's bounds for the Lotka-Nagaev estimator, provided that $(Z_n)_{n \geq 0}$ or $(X_{n,i})_{1 \leq i \leq Z_n}$ can be observed. The results are believed to be optimal or near optimal.
主讲人简介
Xiequan Fan is an associate professor at Center for Applied Mathematics, Tianjin University. He received his Ph.D. degree in Probability theory and Mathematical Statistics from University of South Brittany, France in 2013. His research interests include deviation inequalities, Cramer moderate deviations, Berry-Esseen’s bounds and self-normalized limit theory for martingales and their applications.
