报告题目：Change-Point Detection and Support Recovery for Spatially Indexed Functional Data
时 间：2025年6月16日（星期一）9：30
地 点：科研楼18号楼1102
主 办：数学与统计学院、分析数学及应用教育部重点实验室、统计学与人工智能福建省高校重点实验室
参加对象：感兴趣的老师和学生
报告摘要：Large volumes of spatiotemporal data, characterized by high spatial and temporal variability, may experience structural changes over time. Unlike traditional change-point problems, each sequence in this context consists of function-valued curves observed at multiple spatial locations, with typically only a small subset of locations affected. This paper addresses two key issues: detecting the global change-point and identifying the spatial support set, within a unified framework tailored to spatially indexed functional data. By leveraging a weakly separable cross-covariance structure—an extension beyond the restrictive assumption of space-time separability—we incorporate functional principal component analysis into the change-detection methodology, while preserving common temporal features across locations. A kernel based test statistic is further developed to integrate spatial clustering pattern into the detection process, and its local variant, combined with the estimated change-point, is employed to identify the subset of locations contributing to the mean shifts. To control the false discovery rate in multiple testing, we introduce a functional symmetrized data aggregation approach that does not rely on pointwise p-values and effectively pools spatial information. We establish the asymptotic validity of the proposed change detection and support recovery method under mild regularity conditions. The efficacy of our approach is demonstrated through simulations, with its practical usefulness il lustrated in an application to China’s precipitation data.
报告人简介：梁德才，南开大学统计与数据科学学院副研究员，北京大学统计学博士。主要研究领域为函数型数据分析、时空统计学等。在统计学期刊Journal of the American Statistical Association，Biometrics，Statistica Sinica等发表多篇论文。入选中国科协青年人才托举工程，先后主持国家自然科学基金青年和面上项目。