报告题目：Estimation of functional regression model via functional dimension reduction

报 告 人：王国长 副教授 暨南大学

照    片：

邀 请 人：李本崇

报告时间：2020年12月10日9:30—11:00

腾讯会议ID：155 631 495

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士后工作2年。主要研究方向为：函数型数据分析、充分性降维、时间序列等领域，至今已公开在Journal of Econometrics, Statistics Sinica等国内外知名期刊发表SCI论文近20余篇；主持国家社科基金一般项目、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。

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.