线性回归模型参数的灰色估计理论及应用

Gray Estimation Theory and Application of the Linear Regression Model Parameters

线性回归模型是对随机数据的经典建模模型,但对于非随机的模糊或灰色等不分明性数据如何进行模型构建和统计分析呢?文章在一系列关于灰色统计推断理论的研究基础上,基于灰色系统理论,将灰色估计的基本方法拓展到线性回归模型的参数估计。与经典统计分析方法进行对比,为不分明数据的建模分析提供新的方法。

Linear regression model is a classical model for random data, but how to model and statistically analyze the non-clear data such as non-random fuzzy or gray data and so on？ On the basis of the theory of gray system and a series of researches on the theory of grey statistical inference, this paper extends the basic method of gray estimation to the parameter estimation of the linear regression model. And then the paper makes comparisons between the proposed method and the classical statistical analysis methods, thus providing a new method for modeling and analyzing of the fuzzy data.