In classical regression analysis, the error of independent variable is usually not taken into account in regression analysis. This paper presents two solution methods for the case that both the independent and the dep...In classical regression analysis, the error of independent variable is usually not taken into account in regression analysis. This paper presents two solution methods for the case that both the independent and the dependent variables have errors. These methods are derived from the condition-adjustment and indirect-adjustment models based on the Total-Least-Squares principle. The equivalence of these two methods is also proven in theory.展开更多
Ⅰ. INTRODUCTION Let us consider the self-regression forecast model of classical n-order Y<sub>t</sub>=A<sub>0</sub>+A<sub>1</sub>Y<sub>t-1</sub>+…+A<sub>n</su...Ⅰ. INTRODUCTION Let us consider the self-regression forecast model of classical n-order Y<sub>t</sub>=A<sub>0</sub>+A<sub>1</sub>Y<sub>t-1</sub>+…+A<sub>n</sub>Y<sub>t-n</sub>+e. （1.1） This note applies fuzzy set theory to the expansion of（1. 1）, i.e.展开更多
针对多响应的质量设计问题,本文结合似不相关回归(seemingly unrelated regression,SU R)模型与因子效应原则提出了一种新的建模与优化方法.该方法不仅结合S U R模型与因子效应原则筛选出各响应模型的显著性变量,而且运用多变量过程能...针对多响应的质量设计问题,本文结合似不相关回归(seemingly unrelated regression,SU R)模型与因子效应原则提出了一种新的建模与优化方法.该方法不仅结合S U R模型与因子效应原则筛选出各响应模型的显著性变量,而且运用多变量过程能力指数衡量了过程能力满足规格要求程度的水平.此外,该方法还通过贝叶斯抽样技术考虑了模型参数不确定性和预测响应值波动对优化结果的影响.首先,在S U R模型中针对每个变量设置了一个二元变量指示器以考虑因子效应原则,通过所构建的混合二元变量指示器修正了过程响应和试验因子之间的函数关系;其次,通过计算混合二元变量指示器和模型结构的后验概率以识别显著性变量,从而确定最佳的模型结构;然后,在此基础上结合贝叶斯抽样技术构建了一种新的多变量过程能力指数,并通过最大化所构建的多变量过程能力指数获得了最佳的参数设计值;最后,实际案例研究表明:本文所提方法不仅能够有效地筛选出多响应过程的显著性变量,而且能够获得最佳的参数设计值.展开更多
基金supported by the National Nature Science Foundation of China (41174009)
文摘In classical regression analysis, the error of independent variable is usually not taken into account in regression analysis. This paper presents two solution methods for the case that both the independent and the dependent variables have errors. These methods are derived from the condition-adjustment and indirect-adjustment models based on the Total-Least-Squares principle. The equivalence of these two methods is also proven in theory.
文摘Ⅰ. INTRODUCTION Let us consider the self-regression forecast model of classical n-order Y<sub>t</sub>=A<sub>0</sub>+A<sub>1</sub>Y<sub>t-1</sub>+…+A<sub>n</sub>Y<sub>t-n</sub>+e. （1.1） This note applies fuzzy set theory to the expansion of（1. 1）, i.e.
文摘针对多响应的质量设计问题,本文结合似不相关回归(seemingly unrelated regression,SU R)模型与因子效应原则提出了一种新的建模与优化方法.该方法不仅结合S U R模型与因子效应原则筛选出各响应模型的显著性变量,而且运用多变量过程能力指数衡量了过程能力满足规格要求程度的水平.此外,该方法还通过贝叶斯抽样技术考虑了模型参数不确定性和预测响应值波动对优化结果的影响.首先,在S U R模型中针对每个变量设置了一个二元变量指示器以考虑因子效应原则,通过所构建的混合二元变量指示器修正了过程响应和试验因子之间的函数关系;其次,通过计算混合二元变量指示器和模型结构的后验概率以识别显著性变量,从而确定最佳的模型结构;然后,在此基础上结合贝叶斯抽样技术构建了一种新的多变量过程能力指数,并通过最大化所构建的多变量过程能力指数获得了最佳的参数设计值;最后,实际案例研究表明:本文所提方法不仅能够有效地筛选出多响应过程的显著性变量,而且能够获得最佳的参数设计值.
