区间型符号数据回归分析及其应用

Methodology and application of regression analysis of interval-type symbolic data

介绍了符号数据分析方法的基本理论.针对一种最常用的符号数据——区间型符号数据,基于误差传递的理论,提出了区间回归分析的方法.方法包括了线性回归分析和可线性化的非线性回归分析两种情形.讨论了基于Hausdorff距离的区间数距离,基于此定义了回归模型的评价指标.进行了方法的应用研究,选取沪深300指数与中信规模风格指数,从时间维上对其日内数据进行"数据打包",形成区间型符号数据;建立了区间线性回归分析模型,从全局上揭示了两类指数间的相关性.结论表明,与针对点数据的传统回归分析相比,区间型符号数据的回归分析方法不仅实现了样本空间的降维,而且有利于从整体上把握变量之间的内在关系.

The theory of symbolic data analysis （SDA） is introduced first. One type of the most important symbolic data is interval data. The methods of regression analysis of interval-type symbolic data are proposed via error transferring theory. Linear regression analysis and non-linear regression which can be linearized are studied separately. Furthermore, the distance between interval numbers is defined based on Hausdorff distance. And, based upon this, evaluation indices of the regression analysis models are proposed. Finally, appli.eation of the correlation between CSI 300 and style indices of Chinese international trust ＆ investment company （CITIC） is carried out. In this application study, the interval-type symbolic data are obtained by data package of daily indices data. The regression analysis models of the interval-type symbolic data are set up, revealing the overall correlation between the CSI 300 and style indices of CITIC. It is concluded that, comparing with the traditional regression analysis of point data, the regression analysis of interval-type symbolic data can not only reduce the dimension of the sample space, but also grasp the inner relations of the variables.