报告题目：Confidence surfaces for the mean of locally stationary functional time series

报 告 人：吴未迟 副教授 清华大学

报告时间：2021年11月22日 10:00-11:00

报告地点：腾讯会议 ID：514 451 479会议密码：654321

校内联系人：朱复康 fzhu@jlu.edu.cn

报告摘要：The problem of constructing a simultaneous confidence band for the mean function of a locally stationary functional time series $ \{ X_{i,n} (t) \}_{i = 1, \ldots  n}$  is challenging as these bands cannot be built on classical limit theory.  On the one hand, for a fixed argument $t$ of the functions $X_{i,n}$,  the maximum absolute   deviation between an estimate and   the time dependent  regression function exhibits  (after appropriate standardization) an extreme value behaviour with a Gumbel distribution in the limit. On the other hand for stationary functional data, simultaneous confidence bands can be built on classical central theorems for Banach space valued random variables and the limit distribution of the maximum absolute deviation is given by the sup-norm of a Gaussian process. As both limit theorems have different rates of convergence, they are not compatible, and a weak convergence result, which could be used for the construction of a confidence surface in the locally stationary case, does not exist.

In this paper we propose new bootstrap methodology to construct a simultaneous confidence band for the mean function of a locally stationary functional time series, which is motivated by a Gaussian approximation for the maximum absolute deviation.  We prove the validity of our approach by asymptotic theory, demonstrate good finite sample properties by means of a simulation study and illustrate its applicability analyzing a data example.

报告人简介：吴未迟，清华大学统计学研究中心副教授、博士生导师，加拿大多伦多大学统计学博士。英国伦敦大学学院统计系以及德国鲁尔波鸿大学数学系博士后、副研究员。主要从事时间序列、非参数统计的研究，在Annals of Statistics, Bernoulli, Journal of Business and Economic Statistics 等期刊上发表论文多篇。主持自然科学基金青年项目。