Two Stage Estimation and Its Covariance Matrix in Multivariate Seemingly Unrelated Regression System

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.

Driving factors of CO_(2)emissions in South American countries:An application of Seemingly Unrelated Regression model

Carbon emissions have become a critical concern in the global effort to combat climate change,with each country or region contributing differently based on its economic structures,energy sources,and industrial activities.The factors influencing carbon emissions vary across countries and sectors.This study examined the factors influencing CO_(2)emissions in the 7 South American countries including Argentina,Brazil,Chile,Colombia,Ecuador,Peru,and Venezuela.We used the Seemingly Unrelated Regression(SUR)model to analyse the relationship of CO_(2)emissions with gross domestic product(GDP),renewable energy use,urbanization,industrialization,international tourism,agricultural productivity,and forest area based on data from 2000 to 2022.According to the SUR model,we found that GDP and industrialization had a moderate positive effect on CO_(2)emissions,whereas renewable energy use had a moderate negative effect on CO_(2)emissions.International tourism generally had a positive impact on CO_(2)emissions,while forest area tended to decrease CO_(2)emissions.Different variables had different effects on CO_(2)emissions in the 7 South American countries.In Argentina and Venezuela,GDP,international tourism,and agricultural productivity significantly affected CO_(2)emissions.In Colombia,GDP and international tourism had a negative impact on CO_(2)emissions.In Brazil,CO_(2)emissions were primarily driven by GDP,while in Chile,Ecuador,and Peru,international tourism had a negative effect on CO_(2)emissions.Overall,this study highlights the importance of country-specific strategies for reducing CO_(2)emissions and emphasizes the varying roles of these driving factors in shaping environmental quality in the 7 South American countries.

Bayes and empirical Bayes iteration estimators in two seemingly unrelated regression equations

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.

A NEW ESTIMATE OF REGRESSION COEFFICIENTS IN SEEMINGLY UNRELATED REGRESSION SYSTEM

For a seemingly unrelated regression system consisting of m equations, the information contained in all the equations is divided into sample information and additional information, and a new estimate of the regression coefficients is proposed by using successive superposition. More precisely, the following three problems are solved: (ⅰ) a statistic summarized the additional information is constructed, (ⅱ) a procedure which superposes the additional information on the sample information and a new estimate of regression coefficients are proposed, (ⅲ) some properties of the new estimate are established.

TWO-STAGE ESTIMATION FOR SEEMINGLY UNRELATED NONPARAMETRIC REGRESSION MODELS

This paper is concerned with the estimating problem of seemingly unrelated （SU） non- parametric regression models. The authors propose a new method to estimate the unknown functions, which is an extension of the two-stage procedure in the longitudinal data framework. The authors show the resulted estimators are asymptotically normal and more efficient than those based on only the individual regression equation. Some simulation studies are given in support of the asymptotic results. A real data from an ongoing environmental epidemiologie study are used to illustrate the proposed procedure.

AN EFFICIENT PROCEDURE FOR ESTIMATING TWO SEEMINGLY UNRELATED REGRESSIONS

I. INTRODUCTIONConsider the following system of two seemingly unrelated regressions: Y_i=X_iβ_i+ε_i,

Existence of the Uniformly Minimum Risk Unbiased Estimator in Seemingly Unrelated Regression System

For a seemingly Unrelated regression system with the assumption of normality,a necessary and sufficient condition for the existence of the Uniformly Minimum Risk Unbiased (UMRU)estimator of regression coefficients under strictly convex loss is obtained;it is proved that any unbiased estimator can not improve the least squares estimator;it is also shown that no UMRU estimator exists under missing observations.

Statistical Inference on Seemingly Unrelated Single-Index Regression Models

In this article, we consider a class of seemingly unrelated single-index regression models. By taking the contemporaneous correlation among equations into account we construct the weighted estimators （WEs） for unknown parameters of the coefficients and the improved local polynomial estimators for the unknown functions, respectively. We establish the asymptotic normalities of these estimators, and show both of them are more asymptotically efficient than those ignoring the contemporaneous correlation. The performances of the proposed procedures are evaluated through simulation studies.

EFFICIENT ESTIMATION OF SEEMINGLY UNRELATED ADDITIVE NONPARAMETRIC REGRESSION MODELS

This paper is concerned with the estimating problem of seemingly unrelated(SU)nonparametric additive regression models.A polynomial spline based two-stage efficient approach is proposed to estimate the nonparametric components,which takes both of the additive structure and correlation between equations into account.The asymptotic normality of the derived estimators are established.The authors also show they own some advantages,including they are asymptotically more efficient than those based on only the individual regression equation and have an oracle property,which is the asymptotic distribution of each additive component is the same as it would be if the other components were known with certainty.Some simulation studies are conducted to illustrate the finite sample performance of the proposed procedure.Applying the proposed procedure to a real data set is also made.

On Estimating Regression Coefficients in Seemingly Unrelated Regression System

In the system of m （m ≥ 2） seemingly unrelated regressions, we show that the Gauss-Markov estimator （GME） of any regression coefficients has unique simplified form, which exactly equals to the one- step covariance-adjusted estimator of the regression coefficients, and hence we conclude that for any finite k ≥ 2 the k-step covariance-adjusted estimator degenerates to the one-step covariance-adjusted estimator and the corresponding two-stage Aitken estimator has exactly one simplified form. Also, the unique simplified expression of the GME is just the estimator presented in the Theorem 1 of Wang＇ work [1988]. A new estimate of regression coefficients in seemingly unrelated regression system, Science in China, Series A 10, 1033-1040].

ITERATIVE QUASI-LIKELIHOOD FOR SEEMINGLY UNRELATED REGRESSION SYSTEMS

In the seemingly unrelated regression systems, the existing quasi-likelihood is always involved in the difficult problem of calculating inverse of a high order matrix specially for large systems. To avoid this problem, the new quasi-likelihood proposed in this paper is based mainly on a linearly iterative process of some unbiased estimating functions.Some finite sample properties and asymptotic behaviours for this new quasi-likelihood are investigated. These results show that the new quasi-likelihood for parameter of interest is E-sufficient, iteratively efficient and approximately efficient. Some examples are given to illustrate the theoretical results.

Does digitalization mitigate regional inequalities?Evidence from China

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.

Predicting carbon storage of mixed broadleaf forests based on the finite mixture model incorporating stand factors,site quality,and aridity index

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.

Estimating the productive potential of five natural forest types in northeastern China

Background: There is a serious lack of experience regarding the productive potential of the natural forests in northeastern China, which severely limits the development of sustainable forest management strategies for this most important forest region in China. Accordingly, the objective of this study is to develop a first comprehensive system for estimating the wood production for the five dominant forest types.Methods: Based on a network of 384 field plots and using the state-space approach, we develop a system of dynamic stand models, for each of the five main forest types. Four models were developed and evaluated, including a base model and three extended models which include the effects of dominant height and climate variables. The four models were fitted, and their predictive strengths were tested, using the "seemingly unrelated regression"(SUR) technique.Results: All three of the extended models increased the accuracy of the predictions at varying degrees for the five major natural forest types of northeastern China. The inclusion of dominant height and two climate factors(precipitation and temperature) in the base model resulted in the best performance for all the forest types. On average, the root mean square values were reduced by 13.0% when compared with the base model.Conclusion: Both dominant height and climate factors were important variables in estimating forest production. This study not only presents a new method for estimating forest production for a large region, but also explains regional differences in the effect of site productivity and climate.

Characteristics and Determinants of the Proportion of China's Trade by Air

Based on the China Customs Database and the China Industrial Enterprises Database, this paper estimates the proportions of imports and exports by air of Chinese firms and variables that may influence such proportions. Through OLS regression and seemingly unrelated regression(SUR), this paper analyzes the possible determinants of the share of trade by air. Our findings suggest that the TFP of firms is positively correlated with the share of trade by air. The ratio of value-added in exports is positively correlated with the share of imports by air and negatively correlated with the share of exports by air; the average distance of transport is significantly positively correlated with the share of trade by air in full-sample and grouped regressions. Rising TFP increases the share of imports and exports by air the most for processing trade firms, particularly for firms in the eastern region and foreign-funded firms. An increase in the ratio of value-added in exports increases the share of imports by air the most for general trade firms, and also significantly influences the use of air transport by firms in the eastern region and foreign-funded firms. These conclusions offer valuable policy references for promoting trade in various parts of China and especially the inland regions.

The Prediction Analysis of Customer Lifetime Value in Business to Business Enterprise

The measurement of customer assets value has become a significant task in the field of marketing. Although a series of achievements have been formed, the deeper research is still needed in the following aspects： how to build parameter estimation model of various variables based on the interaction among customer assets elements and how to get the scientific and available measured data. In order to solve these problems, this paper, based on the characteristics of customer relationship in Business to Business （B to B） enterprise and the analysis of the variable factors in the interactive models will systematically and practically use the seemingly unrelated regression method to construct three main parameters estimation models in the customer assets measurement model, and prove the feasibility of the model through a case study. Research results show that measurement model system constructed by this method solves the problem of interaction and germination among parameters influencing factors. At the same time, factors concentration simplifies data sources to ensure the reliability and objectivity of the data, and thus improve the accuracy and feasibility of the estimation of customer assets value.

A Decade of Changes in the Transportation of Passengers： What Are the Factors That Affected the Demand？

Ten years of financial stability in Brazilian economy have gone. In this period, the regional transportation of passengers suffered exogenous impacts： economical crises, airport crises and great proportions＇ accidents, as well as impacts which were intern to the system： institutional changes （liberation of tariff promotions, many companies establishing themselves and also coming to bankruptcy）, creation of regulating institutions in the air transportation as well as the land transportation. Theoretically, it is expected that these changes have generated impacts in the demand for trips, since an environment regulated with more flexible prices and higher amounts of companies would generate a competitive environment in which the companies could struggle to attract their demand. On the other hand, the impacts which are exogenous to the system can generate responses in the sense of restoring the balance of demand. Thus, based on the theoretical experience, this article aims at analyzing empirically, through categorical variables, if there were impacts on the demand for regional trips in Brazil due to the internal or external changes. In order to perform this, monthly data from January, 1999 to December, 2009 are utilized and estimates are calculated making use of SUR （seemingly unrelated regressions）. As a result, we have the meaning of the internal and external impacts related to air and land transports, identifying that the worldwide economic crisis generated an impact at the level of the demand for transportation and also that the flexibility of tariffs allowed by ANTT （Ag^ncia Nacional de Transportes Terrestres） had an equal impact on the demand for land transportation.

Existence of SURU estimators in SURE model with special covariance structures

THROUGHOUT this note, the following notations are used: For a matrix A, A】0 means thatA is positive definite symmetric; R （A）, A′and A- stand for the column space, transposeand any g-inverse of A respectively; PA = A （A′A）- A′and PA = Ik - PA, where Ik is theidentity matrix of order k that is the number of rows in A. Rm×n is the totality of m×n realmatrices.

An Empirical Study on Telecommunication Development in the Rural Areas of China 's 12 Western Provinces

This paper studied rural telecom markets in China＇s 12 western provinces with Seemingly Unrelated Regression （SUR） models. Using two regress analysis of telecom business income and rural telephone permeation rate in 12 western provinces, we got some new conclusions such as, the installation and usage of telephones among farmers are affected by several variables, and income is only one of them. According to our data analysis, variables influencing the installation and usage of telephones are not the same. Different variables exert different degrees of influence in the provinces.

Comparing independent climate-sensitive models of aboveground biomass and diame ter grow th with their compatible simultaneous model system for three larch species in China

Accurate estimate of tree biomass is essential for forest management.In recent years,several climate-sensitive allometric biomass models with diameter at breast height(D)as a predictor have been proposed for various tree species and climate zones to estimate tree aboveground biomass(AGB).But the allometric models only account for the potential effects of climate on tree biomass and do not simultaneously explain the influence of climate on D growth.In this study,based on the AGB data from 256 destructively sampled trees of three larch species randomly distributed across the five secondary climate zones in northeastern and northern China,we first developed a climate-sensitive AGB base model and a climate-sensitive D growth base model using a nonlinear least square regression separately.A compatible simultaneous model system was then developed with the climate-sensitive AGB and D growth models using a nonlinear seemingly unrelated regression.The potential effects of several temperature and precipitation variables on AGB and D growth were evaluated.The fitting results of climatic sensitive base models were compared against those of their compatible simultaneous model system.It was found that a decreased isothermality([mean of monthly(maximum temperatureminimum temperature)]/(Maximum temperature of the warmest month-Minimum temperature of the coldest month))and total growing season precipitation,and increased annual precipitation significantly increased the values of AGB;an increase of temperature seasonality(a standard deviation of the mean monthly temperature)and precipitation seasonality(a standard deviation of the mean monthly precipitation)could lead to the increase of D.The differences of the model fitting results between the compatible simultaneous system with the consideration of climate effects on both AGB and D growth and its corresponding climate-sensitive AGB and D growth base models were very small and insignificant(p>0.05).Compared to the base models,the inhere nt correlation of AGB with D was taken into account effectively by the proposed compatible model system developed with the climate-sensitive AGB and D grow th models.In addition,the compatible properties of the estimated AGB and D were also addressed substantially in the proposed model system.