函数型数据分析的研究进展和技术框架

函数型数据分析(Functional Data Analysis,FDA)是1980年以后发展起来的一种基于离散统计数据函数化、进而通过函数型分析刻画更广义和更深刻统计关系的高维数据分析(Multivariate Data Analysis,MDA)方法。FDA的基本思想是由加拿大麦吉尔大学的J.O.Ramsay和牛津大学的B.W.Silverman等人提出并发展起来的,同时多位世界知名统计学者也对此作出了贡献。目前该方法已广泛应用于经济学、生物学、气象学、心理学、工业及其他领域。函数型数据分析的基本思想是把观测到的数据函数看作一个整体,而不仅仅是个体观测值的顺序排列,函数本质上是指数据的内在结构而不是它们直观的外在表现形式。因此,在简要回顾FDA发展历程的基础上,追踪国际国内主要研究动态,简介和评述FDA研究的技术框架以及与传统多元统计分析方法的差异,并试图就FDA在经济学中的应用进行一定剖析。

The Research Development and Technical Framework of Functional Data Analysis

Functional Data Analysis(FDA) has been developed into a Multivariate Statistical Analysis(MSA) method based on thoughts of converting discrete data into functional ones since 1980s,which portrayed more generalized and more profound statistical relationship through the functional analysis.The basic idea of FDA is brought up by James O.Ramsay,a professor of Canada McGill University and Bernard W.Silverman,from Oxford.Many other world-famous scholars have contributed to the idea.The method is now widely used in economics,biology,meteorology,psychology,industry and other fields.Functional Data Analysis regards observed data as a whole,but not just the order of the individual observations.Functions essentially refer to the inner structure of data,but not their intuitive form.This paper briefly reviews the development history of FDA and tracks domestic and international research trends.It introduces the FDA research technical framework and the differences between FDA research technical framework and the traditional method of multivariate statistical analysis.Attention focus on the application of FDA in economics.