基于模糊Cook距离的模糊线性回归模型的统计诊断  

Statistical Diagnostics of Fuzzy Linear Regression Model Based on Fuzzy Cook Distance

作　　者：张爱武[1] 

机构地区：[1]江苏盐城师范学院数学科学学院,江苏盐城224002

出　　处：《模糊系统与数学》2012年第6期137-145,共9页Fuzzy Systems and Mathematics

基　　金：国家自然科学基金资助项目(11171065);江苏省自然科学基金资助项目(BK2011058)

摘　　要：针对确定输入、模糊输出的模糊线性回归分析模型,采用最小二乘法,讨论了模糊线性回归模型的数据删除模型的参数估计,将建立在确定性数据基础上的线性回归模型统计诊断量Cook距离推广到模糊线性回归分析模型中,构造了统计诊断量—模糊Cook距离,通过数值模拟和对实际例子的研究,识别出其中的强影响点,得出与其它方法相同的结论,表明本文构造的统计诊断量是有效的,且应用比其它方法更方便。The parameter estimation on fuzzy linear regression model based on case deletion is surveyed by the least square method with respect to some distance between fuzzy numbers. The input of the model is real numbers and the output is fuzzy numbers. Furthermore, the impact assessment and fuzzy approach degree of the corresponding regression equation are studied by fuzzy linear regression model based on case deletion. Finally, the method of how to distinguish the strong influential point among the real data is obtained, which also shows that the statistic we propose is effective enough.

关 键 词：模糊线性回归模型 数据删除模型 模糊Cook距离 

分 类 号：O212[理学—概率论与数理统计] O159[理学—数学]