光华讲坛——社会名流与企业家论坛第 期

主 题：Identification of Chang-points in Scalar-on-Function Regression函数上标量回归中长点的辨识

主讲人：美国密歇根大学宋学坤教授

主持人：统计学院林华珍教授

时间：2023年12月29日（周五）下午15:00-16:00

举办地点：柳林校区弘远楼408会议室

主办单位：统计研究中心和统计学院 科研处

主讲人简介：

Dr. Song is Professor of Biostatistics at the School of Public Health in the University of Michigan, Ann Arbor. He received his PhD in Statistics from the University of British Columbia, Vancouver, Canada in 1996.  He has published over 200 peer-reviewed papers and graduated 24 PhD students and trained 6 postdoc research fellows.  Dr. Song's current research interests include data integration, distributed inference, high-dimensional data analysis, longitudinal data analysis, mediation analysis, spatiotemporal modeling, and smart health. He collaborates extensively with researchers from nutritional sciences, environmental health sciences, chronic diseases, and nephrology. He is IMS Fellow, ASA Fellow and Elected Member of the International Statistical Institute. Dr. Song now serves as Associate Editor of the Journal of American Statistical Association, the Annals of Applied Statistics, and the Journal of Multivariate Analysis.

宋学坤，美国密歇根大学安娜堡分校公共卫生学院生物统计学教授。1996年获加拿大温哥华英属哥伦比亚大学统计学博士学位。发表论文200余篇，培养博士研究生24名，培养博士后6名。宋教授目前的研究兴趣包括数据集成、分布式推理、高维数据分析、纵向数据分析、中介分析、时空建模和智能健康。他与来自营养科学、环境健康科学、慢性疾病和肾脏病学的研究人员广泛合作。他是国际数理统计学会（IMS）Fellow、美国统计学会（ASA） Fellow和国际统计学会(ISI)的Elected Member。宋教授目前担任the Journal of American Statistical Association、the Annals of Applied Statistics和the Journal of Multivariate Analysis的副主编。

内容简介：

We consider a scalar-on-function regression analysis of physical activity data collected from a wearable device, in which the functional predictor is given by subject’s Occupation-Time curve (OTC) that presents a proportional continuum of time spent at or above varying activity levels. We invoke a mixed integer optimization (MIO) paradigm to formulate a fused estimation method for homogeneity pursuit. This new approach can perform a simultaneous operation of changepoint detection and step-functional parameter estimation. We show through extensive simulation experiments that the proposed MIO methodology enjoys both estimation accuracy and computational efficiency. Under some mild regularity conditions, we establish a finite error bound for the changepoint selection consistency and parameter estimation consistency. We apply the proposed MIO method on a real-world data analysis to assess the influence of physical activity on biological aging.

主讲人考虑对从可穿戴设备收集的身体活动数据进行标量函数回归分析，其中功能预测因子由受试者的职业时间曲线(OTC)给出，该曲线呈现出在不同活动水平上或以上花费的时间的比例连续体。本文引入混合整数优化(MIO)范式，提出了一种均匀性追求的融合估计方法。该方法可以同时进行变点检测和阶跃函数参数估计。主讲人通过大量的仿真实验表明，所提出的MIO方法具有估计精度和计算效率。在一些温和的正则性条件下，建立了变点选择一致性和参数估计一致性的有限误差界。主讲人将提出的MIO方法应用于现实世界的数据分析，以评估体育活动对生物衰老的影响。