报告题目： Sparse Covariance Function Estimation in High Dimensions
报告人：郭绍俊 中国人民大学
报告时间：2022年10月18日(周二) 16:30-18:00
报告地点：中科院数学与系统科学研究院南楼N219；
腾讯会议 ID：899-485-872
内容摘要
Covariance function estimation is a fundamental task in multivariate functional data analysis and arises in many applications. In this talk, we consider estimating sparse covariance functions for high-dimensional functional data, where the number of random functions p is comparable to, or even larger than the sample size n.Aided by the Hilbert--Schmidt norm of functions, we introduce a new class of functional thresholding operators that combine functional versions of thresholding and shrinkage, and propose the adaptive functional thresholding estimator by incorporating the variance effects of individual entries of the sample covariance function into functional thresholding. To handle the practical scenario where curves are partially observed with errors, we also develop a nonparametric smoothing approach to obtain the smoothed adaptive functional thresholding estimator and its binned implementation to accelerate the computation. We investigate the theoretical properties of our proposals when p grows exponentially with n under both fully and partially observed functional scenarios. Finally, we demonstrate that the proposed adaptive functional thresholding estimators significantly outperform the competitors through extensive simulations and the functional connectivity analysis of two neuroimaging datasets.
主讲人简介
郭绍俊，现为中国人民大学统计与大数据研究院长聘副教授。2003年本科毕业于山东师范大学，2008年获得中国科学院数学与系统科学研究院理学博士学位。2008年-2016年任中国科学院数学与系统科学研究院助理研究员。2009年-2010年赴美国普林斯顿大学运筹与金融工程系博士后研究，主要研究方向为高维数据分析。2014-2016年赴英国伦敦经济学院统计系做博士后研究，主要研究大维时间序列建模。目前主要研究方向有：统计学习；非参数及半参数统计建模；生存分析及函数型数据分析等。
