函数型数据回归分析综述  

Review of Regression Analysis for Functional Data

作　　者：丁辉[1] 许文超[1] 朱汉兵 王国长[2] 张涛[3] 张日权[1] DING Hui;XU Wenchao;ZHU Hanbing;WANG Guochang;ZHANG Tao;ZHANG Riquan(School of Statistics,East China Normal University,Shanghai,200062,China;College of Economics,Jinan University,Guangzhou,510632,China;College of Science,Guangxi University of Technology,Liuzhou,545006,China)

机构地区：[1]华东师范大学统计学院,上海200062 [2]暨南大学经济学院,广州510632 [3]广西科技大学理学院,柳州545006

出　　处：《应用概率统计》2018年第6期630-654,共25页Chinese Journal of Applied Probability and Statistics

基　　金：国家自然科学基金项目(批准号:11571112);教育部博士点基金项目(批准号:20130076110004);上海市优秀学科带头人计划(批准号:14XD1401600);高等学校学科创新引智计划(批准号:B14019);华东师范大学研究生出国(境)短期研修专项基金资助

摘　　要：随着计算机储存能力和在线观测技术的提高,当今数据越来越多的以曲线和图像的形式存在.曲线和图像数据两个最显著的特征是高维和相邻数据间高度相关.这些特征使得传统的多元统计分析方法不再适合,而函数型数据在处理曲线和图像数据中具有无可比拟的优势.近年来各种各样的函数型数据分析方法得以发展,其中包括数据的对齐、主成分分析、回归、分类、聚类等.本文主要介绍函数型数据回归分析研究的起源、发展及最新进展.具体地,本文首先介绍函数型数据的概念;其次介绍函数型主成分分析方法;再次着重介绍函数型回归模型的估计、变量选择和检验方法;最后将简要探讨函数型数据未来的可能发展方向.With the advance of computer storage capacity and online observation technique,more and more data are collected with curves and images.The most two important feature of curve and image data are high-dimension and high correlation between adjacent data.Functional data analysis has more advantage in deal with these data,which can not be treated by traditional multivariate statistics methods.Recently,a variety of functional data methods have been developed,including curve alignment,principal component analysis,regression,classification and clustering.In this paper,we mainly introduce the origins,development and recent process of functional data.Specifically,we firstly introduce the notion of functional data.Secondly,functional principal component analysis has been presented.Then,this paper is devoted to introduce estimation,variable selection and hypothesis testing of functional regression models.Lastly,the paper concludes with a brief discussion of future directions.

关 键 词：函数型主成分分析 函数型回归模型 变量选择 假设检验 

分 类 号：O212.7[理学—概率论与数理统计]