基于数据删除的模糊线性回归模型的影响评价  

Impact Assessment for Fuzzy Linear Regression Model Based on Case Deletion

作　　者：张爱武[1] 

机构地区：[1]盐城师范学院数学科学学院,盐城224002

出　　处：《应用概率统计》2012年第6期625-636,共12页Chinese Journal of Applied Probability and Statistics

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

摘　　要：使用模糊数之间的Euclidean距离和Lebesgue距离的最小二乘方法,分别研究了基于数据删除的模糊线性回归模型的参数估计,并对两种距离下的参数估计进行了比较.此模型的输入为实数,输出为模糊数.构造了检验观测数据中强影响点或异常点的统计诊断量—回归方程的估计标准误差,通过对实际数据的研究,识别出其中的强影响点,表明本文所构造统计量是有效的.Least squares method based on Euclidean distance and Lebesgue distance between fuzzy data is used to study parameter estimation of fuzzy linear regression model based on case deletion respectively. And the parameter estimations on two kinds of distance are compared. The input of the above model is real data and output is fuzzy data. The statistical diagnosis -- estimation standard error of regression equations is constructed to test highly influential point or outlier in observation data. At last through identifying highly influential point or outlier in actual data, it shows that the statistic constructed in this paper is effective.

关 键 词：模糊线性回归模型 数据删除模型 估计标准误差 

分 类 号：O212.2[理学—概率论与数理统计]