函数性数据的统计分析:思想、方法和应用

The Statistical Analysis of Functional Data:Thoughts,Methods and the Applications

实际中,越来越多的研究领域所收集到的样本观测数据具有函数性特征,这种函数性数据是融合时间序列和横截面两者的数据,有些甚是曲线或其他函数图像。虽然计量经济学近二十多年来发展的面板数据分析方法,具有很好的应用价值,但是面板数据只是函数性数据的一种特殊类型,且其分析方法太过于依赖模型的线性结构和假设条件等。本文基于函数性数据的普遍特征,介绍一种对其进行分析的全新方法,并率先使用该方法对经济函数性数据进行分析,拓展了函数性数据分析的应用范围。分析结果表明,函数性数据分析方法,较之计量经济学和其他统计方法具有更多的优越性,尤其能够揭示其他方法所不能揭示的数据特征。

In practice, the observed data set that more and more research fields acquired has functional characteristics. The typical data set of this sort consists of time series and cross-sectional data, and some data sets may take on curves or images. Although the analysis methods of econometrics for panel data set has developed recently are of great value to practice, the panel data set is a special type of functional data and the relevant methods rely too much on the linear structure and some assumptions. This paper presents a completely new data analyzing method based on the functional features of data, and is first to use the method to analyze the practical economic data by exploiting the computer program based on MATLAB. This paper has expanded the scope of the applications of functional data analysis and fills in the gaps in this aspect in China. The results indicate that the functional data analysis has advantages over the methods of econometrics and other statistical methods, and that functional data analysis can reveal the data features that the other methods cannot do.