The general linear hypothesis testing problem for multivariate functional data with applications

主讲人：Tianming Zhu

Dr ZHU Tianming received her Ph.D. in Statistics from National University of Singapore. She is currently an Assistant Professor at the National Institute of Education, Nanyang Technological University. Her main research interest is the hypothesis testing problem, specifically for high-dimensional data and for multivariate functional data. She also has rich experience in using deep learning algorithms to solve real-world problems such as synthesizing tabular data using Generative Adversarial Networks and Variational Autoencoder, anomaly detection using Autoencoder and brain MRI classification problem.

1

报告信息

时间 

2025年12月22日（周一） 

10:00

地点 

中国人民大学通州校区

经济学部楼215

2

报告摘要

As technology continues to advance at a rapid pace, the prevalence of multivariate functional data (MFD) has expanded across diverse disciplines, spanning biology, climatology, finance, and numerous other fields of study. Although MFD are encountered in various fields, the development of methods for hypotheses on mean functions, especially the general linear hypothesis testing (GLHT) problem for such data has been limited. In this study, we propose and study a new global test for the GLHT problem for MFD, which includes the one-way multivariate analysis of variance for functional data (FMANOVA), post hoc, and contrast analysis as special cases. The asymptotic null distribution of the test statistic is shown to be a chi-squared-type mixture dependent of eigenvalues of the heteroscedastic covariance functions. The distribution of the chi-squared-type mixture can be well approximated by a three-cumulant matched chi-squared-approximation with its approximation parameters estimated from the data. By incorporating an adjustment coefficient, the proposed test performs effectively irrespective of the correlation structure in the functional data, even when dealing with a relatively small sample size. Additionally, the asymptotic power of the proposed test under a local alternative is established.     Simulation studies and a real data example demonstrate finite-sample performance and broad applicability of the proposed test.

“统计大讲堂”由中国人民大学统计学院与应用统计科学研究中心联合主办，旨在搭建学界与业界的交流平台，促进统计理论与实践的深度融合，推动统计学科研创新，服务国家经济社会发展。作为统计学院人才培养体系的核心组成部分，“统计大讲堂”通过系列学术讲座、专题研讨等形式，为统计学子提供前沿知识传授与学术思维训练，营造开放包容的学术氛围，以培养具有国际视野、创新能力和实践精神的复合型统计人才。