Generalized linear regression model based on functional data analysis
WANG Huiwen1,2, HUANG Lele1,2, WANG Siyang3
1. School of Economics and Management, Beijing University of Aeronautics and Astronautics, Beijing 100083, China;
2. Beijing Key Laboratory of Emergency Support Simulation Technologies for City Operations, Beijing 100083, China;
3. School of Statistics and Mathematics, Central University of Finance and Economics, Beijing 100081, China
Abstract：Functional linear regression model has captured much attention in functional data analysis. By tools in semiparametric and nonparametric statistics, it is proposed to estimate the coefficients in generalized linear regression models with both multivariate scalar covariates and functional covariates. In this framework, the theory of generalized linear model is introduced, and the response variable is not required to be continuous random variable and may be discrete or attribute data, which widely broadens the application of functional linear model by solving the regression problem of predictors with mixed types of multivariate data and functional data. Besides, Logistic regression and Possion regression corresponding to categorical or discrete responses were emphasized, and a reweight algorithm for maximizing the log likelihood function was provided. In the procedure of estimation, functional principal component analysis and B spline were utilized, and the criterion to select the number of basis functions was suggested. The simulation results show that the proposed estimation and test methods are effective.
王惠文, 黄乐乐, 王思洋. 基于函数型数据的广义线性回归模型[J]. 北京航空航天大学学报, 2016, 42(1): 8-12.
WANG Huiwen, HUANG Lele, WANG Siyang. Generalized linear regression model based on functional data analysis. JOURNAL OF BEIJING UNIVERSITY OF AERONAUTICS AND A, 2016, 42(1): 8-12.
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2016, Vol. 42 
