主 题：Metric Kernel Functional Regression Models in Metric Spaces

主讲人：中国科学技术大学王学钦教授

主持人：统计学院林华珍教授

时间：2022年7月13日（周三）上午9:30-10:30

直播平台及会议ID：腾讯会议，ID: 190-681-360

主办单位：统计研究中心和统计学院 科研处

主讲人简介：

王学钦，中国科学技术大学管理学院教授，2003年毕业于纽约州立大学宾汉姆顿分校，教育部高层次人才入选者。现担任教育部高等学校统计学类专业教学指导委员会委员、中国现场统计研究会副理事长、统计学国际期刊JASA等的Associate Editor、高等教育出版社Lecture Notes: Data Science, Statistics and Probability系列丛书的副主编。

内容提要：

When predictors are data objects in a metric space, regression methods suffer from problems of complex geometric structure and heavy computational burden. In this paper, we propose a novel nonlinear metric kernel regression model with metric space-valued predictors. The new metric kernel is positive definite and is dependent on the endowed metric and the probability measure underlying data objects. This characteristic enables it incorporate not only the data structure but also the data allocation. We propose a simple and efficient procedure to estimate the unknown regression function via penalized least squares. We also provide the convergence rate, such as minimax rate, of the estimator, guaranteeing that the regression function can be well approximated in metric spaces. Simulation studies and application of two real data examples, movement data and diffusion tensor imaging data, demonstrate the feasibility and efficiency of the proposed model.