基于灰色理论的线性回归模型的参数理论及应用  

Research on the Parameters Theory and Application of the Linear Regression Model Based on the Gray System

作　　者：李勇[1] 

机构地区：[1]重庆工商大学数学与统计学院,重庆400067

出　　处：《数理统计与管理》2012年第3期440-446,共7页Journal of Applied Statistics and Management

基　　金：国家自然科学基金(10871217);国家社科基金项目(10XGL013);国家社科基金项目(09XTJ002)

摘　　要：线性回归分析是数理统计学的基本内容之一,但传统数理统计学中的线性回归分析,是建立在非模糊的随机数据上的线性回归估计和回归系数检验。而现实经济社会中大量存在含有模糊或灰色等不分明性的数据,面对这类不分明性数据,简单地使用传统的统计分析方法显然是不足取的。要想较为科学合理地分析与决策,需要利用灰色系统的相关理论,应用于随机系统信息,从而建立灰色线性回归估计、预测和灰色回归系数检验的基本理论方法,并把该方法应用于金融分析实例中,与经典线性回归分析方法进行对比,足见灰色线性回归方法能够提供比经典线性回归较多的有效信息,从而提出处理不分明数据新的方法。The linear regression analysis is one of the basic content of mathematical statistics. But the linear regression analysis of classic statistics is based on linear regression analysis and regression coefficient test on the clear random data.While in reality of the social life, many data is unclear, like the fuzzy and the grey and so on. Faced with such unclear data, how to reasonably analysis and judge this kind of data scientifically. Based on the theory of grey system, it establishes the basic theory and method of linear regression analysis,forecast,regression coefficient testing on the random sample information. What is more, this method is applied to the case of financial statistics, and to comparative analysis with classical linear regression analysis. It can be the gray linear regression method can provide more effective information, in order to solve more data with gray system research.

关 键 词：灰色理论 线性回归模型 灰色回归预测 

分 类 号：O212[理学—概率论与数理统计]