As far as the nonlinear regression method is concerned, the condition when both independent and dependent variable take the Fuzzy value, while the parameter, θ∈ΘR m the real value, have been discussed in . But for...As far as the nonlinear regression method is concerned, the condition when both independent and dependent variable take the Fuzzy value, while the parameter, θ∈ΘR m the real value, have been discussed in . But for most of actual conditions, the independent variable generally takes the real value, while both parameter and dependent variable take the Fuzzy value. This paper propounded a method for the latter and its relevant Fuzzy regreession model. In addition the Fuzzy observation, matrix distribution and the rational estimation of modeling parameter have also been discussed. Furthermore, the Max min estimation of modeling parameter and its corresponding calculating sequence have also been offered to and the calculating example shows the method is feasible.展开更多
In order to detect whether the data conforms to the given model, it is necessary to diagnose the data in the statistical way. The diagnostic problem in generalized nonlinear models based on the maximum Lq-likelihood e...In order to detect whether the data conforms to the given model, it is necessary to diagnose the data in the statistical way. The diagnostic problem in generalized nonlinear models based on the maximum Lq-likelihood estimation is considered. Three diagnostic statistics are used to detect whether the outliers exist in the data set. Simulation results show that when the sample size is small, the values of diagnostic statistics based on the maximum Lq-likelihood estimation are greater than the values based on the maximum likelihood estimation. As the sample size increases, the difference between the values of the diagnostic statistics based on two estimation methods diminishes gradually. It means that the outliers can be distinguished easier through the maximum Lq-likelihood method than those through the maximum likelihood estimation method.展开更多
This paper considers the linear model effected by random disturbance,Y=XB+ε,where [~B_ε]～([^(AΘ)_0],VΣ),and ΘTATX TN XAΘΣ.It gives a definition for general admissible estimator of a linear function SΘ + GB of...This paper considers the linear model effected by random disturbance,Y=XB+ε,where [~B_ε]～([^(AΘ)_0],VΣ),and ΘTATX TN XAΘΣ.It gives a definition for general admissible estimator of a linear function SΘ + GB of random regression coefficients and parameters.The necessary and sufficient conditions for LY and LY + C to be general admissible estimators of SΘ + GB in the class of both homogenous and non-homogenous linear estimators are obtained.The conclusion is not dependent of whether or not SΘ + GB is estimable.展开更多
文摘As far as the nonlinear regression method is concerned, the condition when both independent and dependent variable take the Fuzzy value, while the parameter, θ∈ΘR m the real value, have been discussed in . But for most of actual conditions, the independent variable generally takes the real value, while both parameter and dependent variable take the Fuzzy value. This paper propounded a method for the latter and its relevant Fuzzy regreession model. In addition the Fuzzy observation, matrix distribution and the rational estimation of modeling parameter have also been discussed. Furthermore, the Max min estimation of modeling parameter and its corresponding calculating sequence have also been offered to and the calculating example shows the method is feasible.
基金The National Natural Science Foundation of China(No.11171065)the Natural Science Foundation of Jiangsu Province(No.BK2011058)
文摘In order to detect whether the data conforms to the given model, it is necessary to diagnose the data in the statistical way. The diagnostic problem in generalized nonlinear models based on the maximum Lq-likelihood estimation is considered. Three diagnostic statistics are used to detect whether the outliers exist in the data set. Simulation results show that when the sample size is small, the values of diagnostic statistics based on the maximum Lq-likelihood estimation are greater than the values based on the maximum likelihood estimation. As the sample size increases, the difference between the values of the diagnostic statistics based on two estimation methods diminishes gradually. It means that the outliers can be distinguished easier through the maximum Lq-likelihood method than those through the maximum likelihood estimation method.
基金the National Natural Science Foundation of China (No. 40574003)
文摘This paper considers the linear model effected by random disturbance,Y=XB+ε,where [~B_ε]～([^(AΘ)_0],VΣ),and ΘTATX TN XAΘΣ.It gives a definition for general admissible estimator of a linear function SΘ + GB of random regression coefficients and parameters.The necessary and sufficient conditions for LY and LY + C to be general admissible estimators of SΘ + GB in the class of both homogenous and non-homogenous linear estimators are obtained.The conclusion is not dependent of whether or not SΘ + GB is estimable.
