In many real-world problems, observations are usually described by approximate values due to fuzzy uncertainty, unlikeprobabilistic 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.\cite{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.
The project was 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) and the Foundation of Hujiang (Grant No. B14005).
引用本文:
张雪玲; 陆秋君. 具有模糊随机误差的回归模型的参数估计[J]. 应用概率统计, 2020, 36(6): 586-604.
ZHANG Xueling; LU Qiujun. Parameter Estimation of Multivariate Regression Model with Fuzzy Random Errors. CHINESE JOURNAL OF APPLIED PROBABILITY AND STATIST, 2020, 36(6): 586-604.