Multivariate seemingly unrelated regression system is raised first and the two stage estimation and its covariance matrix are given. The results of the literatures[1-5] are extended in this paper.
For the two seemingly unrelated regression system, this paper proposed a new type of estimator called pre-test principal components estimator (PTPCE) and discussed some properties of PTPCE.
Regional inequality significantly influences sustainable development and human well-being.In China,there exists pronounced regional disparities in economic and digital advancements;however,scant research delves into t...Regional inequality significantly influences sustainable development and human well-being.In China,there exists pronounced regional disparities in economic and digital advancements;however,scant research delves into the interplay between them.By analyzing the economic development and digitalization gaps at regional and city levels in China,extending the original Cobb-Douglas production function,this study aims to evaluate the impact of digitalization on China's regional inequality using seemingly unrelated regression.The results indicate a greater emphasis on digital inequality compared to economic disparity,with variable coefficients of 0.59 for GDP per capita and 0.92 for the digitalization index over the past four years.However,GDP per capita demonstrates higher spatial concentration than digitalization.Notably,both disparities have shown a gradual reduction in recent years.The southeastern region of the Hu Huanyong Line exhibits superior levels and rates of economic and digital advancement in contrast to the northwestern region.While digitalization propels economic growth,it yields a nuanced impact on achieving balanced regional development,encompassing both positive and negative facets.Our study highlights that the marginal utility of advancing digitalization is more pronounced in less developed regions,but only if the government invests in the digital infrastructure and education in these areas.This study's methodology can be utilized for subsequent research,and our findings hold the potential to the government's regional investment and policy-making.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
The diameter distribution function(DDF)is a crucial tool for accurately predicting stand carbon storage(CS).The current key issue,however,is how to construct a high-precision DDF based on stand factors,site quality,an...The diameter distribution function(DDF)is a crucial tool for accurately predicting stand carbon storage(CS).The current key issue,however,is how to construct a high-precision DDF based on stand factors,site quality,and aridity index to predict stand CS in multi-species mixed forests with complex structures.This study used data from70 survey plots for mixed broadleaf Populus davidiana and Betula platyphylla forests in the Mulan Rangeland State Forest,Hebei Province,China,to construct the DDF based on maximum likelihood estimation and finite mixture model(FMM).Ordinary least squares(OLS),linear seemingly unrelated regression(LSUR),and back propagation neural network(BPNN)were used to investigate the influences of stand factors,site quality,and aridity index on the shape and scale parameters of DDF and predicted stand CS of mixed broadleaf forests.The results showed that FMM accurately described the stand-level diameter distribution of the mixed P.davidiana and B.platyphylla forests;whereas the Weibull function constructed by MLE was more accurate in describing species-level diameter distribution.The combined variable of quadratic mean diameter(Dq),stand basal area(BA),and site quality improved the accuracy of the shape parameter models of FMM;the combined variable of Dq,BA,and De Martonne aridity index improved the accuracy of the scale parameter models.Compared to OLS and LSUR,the BPNN had higher accuracy in the re-parameterization process of FMM.OLS,LSUR,and BPNN overestimated the CS of P.davidiana but underestimated the CS of B.platyphylla in the large diameter classes(DBH≥18 cm).BPNN accurately estimated stand-and species-level CS,but it was more suitable for estimating stand-level CS compared to species-level CS,thereby providing a scientific basis for the optimization of stand structure and assessment of carbon sequestration capacity in mixed broadleaf forests.展开更多
For a system of two seemingly unrelated regression equations given by (?)(y_1 is an m×1 vector and y_2 is an n×1 vector,m≠n),employ- ing the covariance adjusted technique,we propose the parametric Bayes and...For a system of two seemingly unrelated regression equations given by (?)(y_1 is an m×1 vector and y_2 is an n×1 vector,m≠n),employ- ing the covariance adjusted technique,we propose the parametric Bayes and empirical Bayes iteration estimator sequences for regression coefficients.We prove that both the covariance matrices converge monotonically and the Bayes iteration estimator squence is consistent as well.Based on the mean square error (MSE) criterion,we elaborate the su- periority of empirical Bayes iteration estimator over the Bayes estimator of single equation when the covariance matrix of errors is unknown.The results obtained in this paper further show the power of the covariance adiusted approach.展开更多
基金Supported by the NSF of Henan Province(0611052600)
文摘Multivariate seemingly unrelated regression system is raised first and the two stage estimation and its covariance matrix are given. The results of the literatures[1-5] are extended in this paper.
文摘For the two seemingly unrelated regression system, this paper proposed a new type of estimator called pre-test principal components estimator (PTPCE) and discussed some properties of PTPCE.
基金funded by National Natural Science Foundation of China(Grants No.42171210,42371194)Major Project of Key Research Bases for Humanities and Social Sciences Funded by the Ministry of Education of China(Grant No.22JJD790015).
文摘Regional inequality significantly influences sustainable development and human well-being.In China,there exists pronounced regional disparities in economic and digital advancements;however,scant research delves into the interplay between them.By analyzing the economic development and digitalization gaps at regional and city levels in China,extending the original Cobb-Douglas production function,this study aims to evaluate the impact of digitalization on China's regional inequality using seemingly unrelated regression.The results indicate a greater emphasis on digital inequality compared to economic disparity,with variable coefficients of 0.59 for GDP per capita and 0.92 for the digitalization index over the past four years.However,GDP per capita demonstrates higher spatial concentration than digitalization.Notably,both disparities have shown a gradual reduction in recent years.The southeastern region of the Hu Huanyong Line exhibits superior levels and rates of economic and digital advancement in contrast to the northwestern region.While digitalization propels economic growth,it yields a nuanced impact on achieving balanced regional development,encompassing both positive and negative facets.Our study highlights that the marginal utility of advancing digitalization is more pronounced in less developed regions,but only if the government invests in the digital infrastructure and education in these areas.This study's methodology can be utilized for subsequent research,and our findings hold the potential to the government's regional investment and policy-making.
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.
基金funded by the National Key Research and Development Program of China(No.2022YFD2200503-02)。
文摘The diameter distribution function(DDF)is a crucial tool for accurately predicting stand carbon storage(CS).The current key issue,however,is how to construct a high-precision DDF based on stand factors,site quality,and aridity index to predict stand CS in multi-species mixed forests with complex structures.This study used data from70 survey plots for mixed broadleaf Populus davidiana and Betula platyphylla forests in the Mulan Rangeland State Forest,Hebei Province,China,to construct the DDF based on maximum likelihood estimation and finite mixture model(FMM).Ordinary least squares(OLS),linear seemingly unrelated regression(LSUR),and back propagation neural network(BPNN)were used to investigate the influences of stand factors,site quality,and aridity index on the shape and scale parameters of DDF and predicted stand CS of mixed broadleaf forests.The results showed that FMM accurately described the stand-level diameter distribution of the mixed P.davidiana and B.platyphylla forests;whereas the Weibull function constructed by MLE was more accurate in describing species-level diameter distribution.The combined variable of quadratic mean diameter(Dq),stand basal area(BA),and site quality improved the accuracy of the shape parameter models of FMM;the combined variable of Dq,BA,and De Martonne aridity index improved the accuracy of the scale parameter models.Compared to OLS and LSUR,the BPNN had higher accuracy in the re-parameterization process of FMM.OLS,LSUR,and BPNN overestimated the CS of P.davidiana but underestimated the CS of B.platyphylla in the large diameter classes(DBH≥18 cm).BPNN accurately estimated stand-and species-level CS,but it was more suitable for estimating stand-level CS compared to species-level CS,thereby providing a scientific basis for the optimization of stand structure and assessment of carbon sequestration capacity in mixed broadleaf forests.
基金supported by the National Natural Science Foundation of China(Grant No.10271001).
文摘For a system of two seemingly unrelated regression equations given by (?)(y_1 is an m×1 vector and y_2 is an n×1 vector,m≠n),employ- ing the covariance adjusted technique,we propose the parametric Bayes and empirical Bayes iteration estimator sequences for regression coefficients.We prove that both the covariance matrices converge monotonically and the Bayes iteration estimator squence is consistent as well.Based on the mean square error (MSE) criterion,we elaborate the su- periority of empirical Bayes iteration estimator over the Bayes estimator of single equation when the covariance matrix of errors is unknown.The results obtained in this paper further show the power of the covariance adiusted approach.
