不同距离的双线性自适应模糊回归的最小二乘比较  

Least Squares Comparison between Different Distances from the Doubly Linear Adaptive Fuzzy Regression

作　　者：张爱武[1] 

机构地区：[1]盐城师范学院数学科学学院,江苏盐城224002

出　　处：《数学的实践与认识》2013年第19期146-155,共10页Mathematics in Practice and Theory

基　　金：国家自然科学基金(11071207);江苏省自然科学基金(BK2011058)

摘　　要：针对双线性自适应模糊回归模型,采用了欧氏距离、Y-K距离和D_k距离,分别讨论了该模型的最小二乘估计及相关性质,得出在这三种距离下,它们的回归系数的最小二乘估计的形式是一致的仅仅系数不相同,且它们的观测中心和插入中心、设计边宽和插入边宽的误差和为0的结论.通过实例验证了上述结论的正确性.Euclidean distance, Y-K distance and Dk distance are used respectively to study the least squares estimation and the corresponding property of the Doubly Linear adaptive fuzzy regression model. Under the above three distance, the form of the least squares estimation of regression coefficients is the same, only different form their coefficients. And the error sum of the observation center and insert center is zero. So as design edge width and insert edge width. The validity of the conclusion is proved through the example.

关 键 词：模糊线性回归 欧氏距离 Y-K距离 D_k距离 最小二乘估计 

分 类 号：O212.1[理学—概率论与数理统计]