报告题目：Estimation and Optimal Structure Selection of High-Dimensional Toeplitz Covariance Structure
主讲人：潘建新教授（英国曼彻斯特大学）
时间：2020年1月2日（周四）15:30 p.m.
地点：北院卓远楼305会议室
主办单位：统计与数学学院
摘要：The estimation of structured covariance matrix arises in many applications. An appropriate covariance structure improves the accuracy of covariance estimation and increases the efficiency of the mean parameter estimation in statistical models. For example, a good estimation of covariance structures leads to accurate trajectory predictions for longitudinal data and time series data. In this paper we propose a novel statistical method that is able to select the optimal Toeplitz structure and estimate the high-dimensional covariance matrix simultaneously. Entropy loss functions with nonconvex penalties are employed as matrix-discrepancy measures, under which the optimal covariance structure and the selection of the associated Toeplitz structures are made, simultaneously. The resulting Toeplitz structured covariance estimators are guaranteed to be positive definite, unbiased and selection consistent. Asymptotic theories are derived and simulation studies are conducted, showing a very high accurate Toeplitz covariance structure estimation. The proposed method is also applied to real data practices, demonstrating its good performance in covariance estimation in practice.
主讲人简介：
潘建新教授，英国曼彻斯特大学(University of Manchester)数学学院终身教授，英国伦敦图灵数据科学研究院（The Turing Institute)研究员，英国皇家统计学会(The Royal Statistical Society) 会士（Fellow）, 国际统计学会（International Statistical Institute）当选会员（elected member）和美国数理统计学会（Institute of Mathematical Statistics）会员。统计学杂志Biometrics、Biometrical Journal 及Journal of Multivariate Analysis 编委（Associated Editor）。1996年在香港浸会大学获得统计学博士学位，之后到英国洛桑(Rothamsted)实验中心从事博士后研究。2002年10月加盟曼彻斯特大学数学学院，先后仼讲师(2002)、高级讲师(2004)、Reader(2005)。2006年被曼彻斯特大学聘为终身教授，并兼任曼彻斯特大学医学院研究员。曾担任曼大数学学院概率统计系系主任。致力于统计学领域内复杂数据模型的理论研究及其在医学、金融及工业上的应用，取得了多项创新性研究成果。成果发表在包括Journal of the American Statistical Association和Biometrika在内的统计学主流期刊上。已发表学术论文100余篇，出版学术专著2部(Growth Curve Models and Statistical Diagnostics 和 Case-Deletion Diagnostics in Linear Mixed Models)，其中1部于2002年由Springer出版社出版。已指导18名博士研究生并获得学位。
