函数型数据广义线性模型和分类问题综述  

Review of Generalized Linear Models and Classification for Functional Data

作　　者：白德发[1] 徐欣 王国长[2] BAI Defa;XU Xin;WANG Guochang(Office of Scientific R&D,Jinan University,Guangzhou Guangdong 510632,China;College of Economics,Jinan University,Guangzhou Guangdong 510632,China)

机构地区：[1]暨南大学地方研究总院,广东广州510632 [2]暨南大学经济学院,广东广州510632

出　　处：《广西师范大学学报（自然科学版）》2022年第1期15-29,共15页Journal of Guangxi Normal University:Natural Science Edition

基　　金：国家社会科学基金(20BTJ041)。

摘　　要：函数型数据采用全非参数的方法,假设数据来自一条光滑的曲线,把整个曲线当成一个样本来处理,从而避免高维和高度相关的问题。其研究始于20世纪50年代,经过近70多年来的发展,很多经典的统计分析方法都被推广到函数型数据,且被中外学者写成综述和相关书籍以便研究者使用,如主成分、典型相关、线性模型和聚类问题等。但是,目前仍缺少有关函数广义线性模型和分类问题的综述和书籍。基于此,本文从函数型数据发展的数据形式、函数近似包括基底展开和主成分、函数广义线性模型和分类等问题的发展历程及未来发展方向等方面进行详细的综述。进一步,为了能够在经济、金融、医学、气象和环境等领域更好地应用函数型数据,本文提供了具体的样条估计计算程序。The all non-parametric method suppose that functional data comes from a smooth curve.The whole curve is treated as a sample to avoid the problems of high dimension and high correlation.The research of functional data began in 1950s.After more than 100 years of development,many classical statistical analysis methods have been extended to functional data,and written in review and related books by Chinese and foreign scholars for other researchers to use,such as principal component,typical correlation,linear model and clustering problems.However,there are few books and reviews about generalized linear models and classification for functional data.This article gives a detailed review of the development process and future development directions of the functional data analysis and the function approximation,including the basis expansion and principal components,the generalized linear model and classification of functional data.Furthermore,in order to better apply functional data in the fields of economy,finance,medicine,meteorology and environment,some specific calculation programs for the B-spline are provided in this article.

关 键 词：函数型数据 广义线性模型 分类 函数主成分分析 函数线性模型 

分 类 号：O212.7[理学—概率论与数理统计]