报告题目：基于函数充分降维的函数线性模型估计

报 告 人：王国长副教授  暨南大学

报告时间：2020年7月4日 上午 11:30-12:30

报告地点：腾点击链接入会，或添加至会议列表：

https://meeting.tencent.com/s/IjnNY3jilUiF

会议 ID：679 370 315

校内联系人：赵世舜 zhaoss@jlu.edu.cn

报告摘要：

The functional linear regression model corresponding to a scalar response and a functional predictor is becoming increasingly common. Since the predictor is infinite dimensional, some form of dimension reduction is essential. There are two popular dimension reduction methods such as expanding the functional predictor or regression parameter function on the functional principal component basis or on a fixed bases (such as B-spline, Wavelet). In the present paper, we estimate the functional linear model by using the functional sufficient dimension reduction (FSDR) basis. Compared to the existing methods, the proposed method is appealing because the FSDR basis is related to both the functional predictor and the response variable, whereas the functional principal component basis is only related to the functional predictor and the fixed basis (B-spline, Wavelet) is independent from both the functional predictor and the response variable. Our techniques involve methods for giving a new expansion for the predictor, for giving a specific expression for the regression parameter function, for estimating the FSDR space by a new method and some asymptotical properties about the regression parameter function and the prediction for the test samples. Numerical studies, including both simulation studies and applications on real-life data, are presented to demonstrate the accuracy of the proposed method.

报告人简介：

王国长，暨南大学经济学院统计学系副教授，于2012年获东北师范大学统计学博士学位，中科院数学与系统科学研究院从事博后工作2年。主要研究方向为：函数型数据分析、充分性降维、时间序列和机器学习等领域，至今已公开发表SCI论文近20余篇；主持国家自然科学基金青年基金、博士后面上项目、广东省自然科学基金面上项目各一项。