Seminar by Prof. Xiaofeng SHAO from Department of Statistics, University of Illinois at Urbana-Champaign

Statistical analysis of object-valued data that reside in a metric space is gradually emerging as an important branch of functional data analysis in statistics. Notable examples include networks, distributions and covariance matrices. Many object-valued data are collected as a time series, such as yearly age-at-death distributions for countries in Europe and daily Pearson correlation matrices for several cryptocurrencies. In this talk we introduce some recent work on statistical inference for these non-Euclidean time series. Specifically, we will cover change-point detection and serial independence testing. For both problems, our test statistics only depend on pairwise distance between two random objects and involve less number of tuning parameters than existing counterparts. The asymptotic theory will be presented to justify the validity of our proposed testing and estimation methods. Simulation results and real data applications are showcased to demonstrate the efficacy and versatility of our proposed procedures.

Professor Shao Xiaofeng received his PhD degree in Statistics from the University of Chicago in 2006 and has since been a faculty member with the Department of Statistics at the University of Illinois Urbana-Champaign. His current research interests include time series analysis, change-point analysis, functional data analysis, high dimensional data analysis and their applications. He is a fellow of Institute of Mathematical Statistics (IMS) and American Statistical Association (ASA). He currently serves as an associate editor for Journal of Royal Statistical Society, Series B, Journal of the American Statistical Association and Journal of Time Series Analysis.