摘要
由于现实世界问题内在的复杂性和可变性,不同于概率不确定性,大量模糊不确定信息难以从试验得到其准确的信息,联合采用统计模型与模糊集理论有助于提高对复杂系统的辨识和分析.本文针对具有模糊输入、模糊输出和模糊随机误差项的多元线性回归模型,运用基于模糊数扩张理论的最小二乘法,研究模型参数的解析表达式.本文是文献[21]模型的推广,基于模糊数间完备距离得到多元情形下回归模型清晰参数的最小二乘估计.本文探讨了该估计量的大样本性质、渐近相对效率和回归参数的置信域,证明了多元情形下估计量的渐近正态性和相合性.另外,文中将模糊变量进行统一设定规避了文献[21]对模糊随机误差项作端点设定引致的计算不便和负展形问题.最后,本文通过随机数值试验模拟来探究两个自变量情形下回归参数模糊最小二乘估计的样本性质和置信域.
In many real-world problems,observations are usually described by approximate values due to fuzzy uncertainty,unlike probabilistic uncertainty that has nothing to do with experimentation.The combination of statistical model and fuzzy set theory is helpful to improve the identification and analysis of complex systems.As an extension of statistical techniques,this study is an investigation of the relationship between fuzzy multiple explanatory variables and fuzzy response with numeric coefficients and the fuzzy random error term.In this work we describe a parameter estimation procedure carrying out the least-squares method in a complete metric space of fuzzy numbers to determine the coefficients based on the extension principle.We demonstrate how the fuzzy least squares estimators present large sample statistical properties,including asymptotic normality,strong consistency and confidence region.The estimators are also examined via asymptotic relative efficiency concerning traditional least squares estimators.Different from the construction of error term in Kim et al.[21],it is more reasonable in the proposed model since the problems of inconsistency in referring to fuzzy variable and producing the negative spreads may be avoided.The experimental study verifies that the proposed fuzzy least squares estimators achieve the meaning consistent with the theory identification for large sample data set and better generalization regarding one single variable model.
作者
张雪玲
陆秋君
ZHANG Xueling;LU Qiujun(College of Science,University of Shanghai for Science and Technology,Shanghai,200093,China)
出处
《应用概率统计》
CSCD
北大核心
2020年第6期586-604,共19页
Chinese Journal of Applied Probability and Statistics
基金
supported by the First-Class Discipline(System Science)Construction Project of Shanghai Province(Grant No.XTKX2012)
the Priority Discipline Project of Shanghai Province(Grant No.T0502)
the Foundation of Hujiang(Grant No.B14005)。
关键词
最小二乘估计
模糊数
渐近性质
模糊随机误差
fuzzy least squares estimator
fuzzy number
asymptotic properties
fuzzy random error
