Bootstrap Massive and Chaotic Data

主讲人：Nan Zou, Macquarie University

主持老师：（北大经院）王熙

参与老师：  （北大经院）王一鸣、王法、刘蕴霆

（北大国发院）黄卓、张俊妮、孙振庭、

（北大新结构）胡博

时间：2024年5月17日（周五） 10:00-11:30

地点（线上）：   Zoom 会议链接：

https://us06web.zoom.us/j/88157086216?pwd=CqDip6UGwQPifM9s1izvaHXyoglQZL.1

会议号: 881 5708 6216

密码: 990080

报告摘要：

This talk contains two parts. Its first part investigates the “bag of little bootstraps”, a bootstrap designed for massive data. In classic statistical inference, the bootstrap stands out as a simple, powerful, and data-driven technique. However, when coping with massive data sets, which are increasingly prevalent these days, the bootstrap can be computationally infeasible. To speed up the bootstrap for massive data sets, the bag of little bootstraps was invented in 2014. Despite its considerable popularity, little is known about the bag of little bootstraps’s theoretical properties, including reliability. Indeed, our preliminary results have already raised questions on the applicability of the bag of little bootstraps under a simple but important setting. This part will first introduce the bag of little bootstraps procedure and then investigate its theoretical applicability. Specifically, for this applicability, this part will present a counterexample for the claimed sufficient condition in the literature and will, as a remedy, provide a (hopefully) correct, generic sufficient condition. This part is joint with L. Peng, P. Bertail, D. Politis, H. Shang, and S. Volgushev.

This talk’s second part introduces the bootstrap for chaotic dynamical systems. After its establishment in the late 19th century through the efforts of Poincaré and Lyapunov, the theory of dynamical systems was applied to study processes that change over time. Despite their deterministic nature, dynamical systems can exhibit incomprehensibly chaotic behaviors and seemingly random patterns. Consequently, a dynamical system is usually represented by a probabilistic model, in which the unknown parameters must be estimated using statistical methods. To measure the uncertainty of such estimation, we develop a bootstrap method and establish its consistency and second-order efficiency via continuous Edgeworth expansions. This part is joint with K. Fernando.

主讲人简介：

Dr Nan Zou is a lecturer in Statistics, School of Mathematical and Physical Science, Macquarie University. His research interests lie in Empirical process, Time series analysis, Extreme value theory, Resampling-type method, Statistical inference of massive datasets and Statistical inference of dynamical systems. Dr Nan Zou has published papers in Annals of Statistics, Econometrics and Statistics, Journal of Multivariate Analysis, Journal of Nonparametric Statistics and Statistics and Probability Letters.