题目：Statistical Inference for Change-Points in High-Dimensional Data和Testing for the martingale difference hypothesis in multivariate time series models

主讲人： 伊利诺伊大学香槟分校 邵晓峰教授

主持人：统计学院 常晋源教授

时间：2022年6月21日（周二）上午9:30-11:30

直播平台及会议ID：腾讯会议，312 244 990

报告一：Statistical Inference for Change-Points in High-Dimensional Data

报告摘要：

Change point detection for high-dimensional data has wide applications in many disciplines, such as biological science, economics and finance. In this talk, I will review some recent work on U-statistic based approach by my group. The topics I plan to cover include: a L_2 norm based test statistic for both high-dimensional independent and dependent data; a L_q norm based test statistic for high-dimensional independent data.  Both asymptotic theory and numerical results will be presented to illustrate the usefulness of the proposed test statistics. Some future directions will be mentioned as well.

报告二：Testing for the martingale difference hypothesis in multivariate time series models

报告摘要：

This talk proposes a general class of tests to examine whether the error term is a martingale difference sequence in a multivariate time series model with parametric conditional mean. These new tests are formed based on recently developed martingale difference divergence matrix (MDDM), and they provide formal tools to test the multivariate martingale hypothesis in the literature for the first time. Under suitable conditions, the asymptotic null distributions of these MDDM-based tests are established. Moreover, these MDDM-based tests are consistent to detect a broad class of fixed alternatives, and have nontrivial power against local alternatives of order n^-1/2, where n is the sample size. Since the asymptotic null distributions depend on the data generating process and the parameter estimation, a wild bootstrap procedure is further proposed to approximate the critical values of these MDDM-based tests, and its theoretical validity is justified. Finally, the usefulness of these MDDM-based tests is illustrated by simulation studies and one real data example.

主讲人简介：

Dr. Shao is Professor of Statistics and PhD program director, at the Department of Statistics, University of Illinois at Urbana-Champaign (UIUC). He received his PhD in Statistics from University of Chicago in 2006 and has been on the UIUC faculty since then. Dr. Shao's research interests include time series analysis, high-dimensional data analysis, functional data analysis, change-point analysis, resampling methods and asymptotic theory. He is an elected ASA and IMS fellow.