学术报告：Functional Data Analysis in High Dimensions: Covariance Information and Phase Transition

报告时间：2023年10月24日（星期二）下午14:00-15:00

报告地点：沙河校区，二教212

报告人：郭绍俊，中国人民大学统计与大数据研究院，副教授

报告摘要：In this talk, we will discuss two problems that focus on improving the estimation accuracy of the covariance function and understanding phase transition phenomena in high dimensions. The first problem deals with 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. To address this, we propose the adaptive functional thresholding estimator. Additionally, in order to handle the practical scenario where curves are partially observed with errors, we also develop a nonparametric smoothing version and its binned implementation to accelerate computation. The second problem revisits the phase transition phenomena from a nonasymptotic perspective. Estimating the mean and covariance functions nonparametrically is widely used in functional data analysis, with local linear smoothing techniques being the most frequently employed. Building upon the work of Zhang and Wang (2016), who explored the asymptotic properties of estimation, we investigate phase transition phenomena based on the relative order of the average sampling frequency per subject, T, to the number of subjects, n. This also allows us to partition the data into three categories: "sparse", "semi-dense", and "ultra-dense". In the context of high-dimensional scenarios, we derive comprehensive concentration inequalities for the local linear smoothers. We then investigate the scaled phase transitions and the corresponding elementwise maximum rates from sparse to semi-dense to ultra-dense functional data in high dimensions, taking into account the presence of extra log p terms to account for the high-dimensional effect.

报告人简介：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。2008-2016年任中国科学院数学与系统科学研究院助理研究员。2009-2010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；高维生存分析及函数型数据分析等。研究成果发表于Journal of Royal Statistical Society Series B, Journal of the American Statistical Association, Biometrika, Bernoulli, Journal of Econometrics, Journal of Business and Economic Statistics等期刊上。

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