一、报告时间

2025年05月08日09:00

二、报告形式

腾讯会议：508 795 220

三、报告人

姓名：桑培俊   单位： 加拿大滑铁卢大学

四、报告主题

Determine the Order of Functional Data

五、报告摘要

Dimension reduction is often necessary in functional data analysis, with functional principal component analysis being one of the most widely used techniques. A key challenge in applying these methods is determining the number of eigen-pairs to retain, a problem known as order determination. When a covariance function admits a finite representation, the challenge becomes estimating the rank of the associated covariance operator. While this problem is straightforward when the full trajectories of functional data are available, in practice, functional data are typically collected discretely and are subject to measurement error contamination. This contamination introduces a ridge to the empirical covariance function, which obscures the true rank of the covariance operator. We propose a novel procedure to identify the true rank of the covariance operator by leveraging the information of eigenvalues and eigenfunctions. By incorporating the nonparametric nature of functional data through smoothing techniques, the method is applicable to functional data collected at random, subject-specific points. Extensive simulation studies demonstrate the excellent performance of our approach across a wide range of settings, outperforming commonly used information-criterion-based methods and maintaining effectiveness even in high-noise scenarios. We further illustrate our method with two real-world data examples.

六、报告人简介

桑培俊，加拿大滑铁卢大学副教授。主要研究方向是函数型数据分析回归模型中的统计推断问题以及实时函数型数据的回归问题，以及Positive-unlabeled learning和ROC曲线分析。在统计专业国际顶刊Biometrika, Biometrics, Statistica Sinica, Journal of Computational and Graphical Statistics等发表多篇高水平学术论文，主持多项基金项目。