Best linear unbiased predictors and estimators under a pair of constrained seemingly unrelated regression models

2020 ◽  
Vol 158 ◽  
pp. 108669 ◽  
Author(s):  
Hong Jiang ◽  
Jianwei Qian ◽  
Yuqin Sun
Keyword(s):  
Regression Models ◽  
Seemingly Unrelated Regression ◽  
Unrelated Regression ◽  
Best Linear Unbiased

scholarly journals Some remarks on a pair of seemingly unrelated regression models

2019 ◽  
Vol 17 (1) ◽  
pp. 979-989 ◽  
Author(s):  
Jian Hou ◽  
Yong Zhao
Keyword(s):  
Linear Regression ◽  
Regression Models ◽  
Sufficient Conditions ◽  
Seemingly Unrelated Regression ◽  
Regression Equations ◽  
Linear Regression Models ◽  
Unknown Parameters ◽  
Unrelated Regression ◽  
Best Linear Unbiased ◽  
Best Linear Unbiased Estimators

Abstract Linear regression models are foundation of current statistical theory and have been a prominent object of study in statistical data analysis and inference. A special class of linear regression models is called the seemingly unrelated regression models (SURMs) which allow correlated observations between different regression equations. In this article, we present a general approach to SURMs under some general assumptions, including establishing closed-form expressions of the best linear unbiased predictors (BLUPs) and the best linear unbiased estimators (BLUEs) of all unknown parameters in the models, establishing necessary and sufficient conditions for a family of equalities of the predictors and estimators under the single models and the combined model to hold. Some fundamental and valuable properties of the BLUPs and BLUEs under the SURM are also presented.

scholarly journals Building W Matrices Using Selected Geostatistical Tools: Empirical Examination and Application

Stats ◽  
2018 ◽  
Vol 1 (1) ◽  
pp. 112-133 ◽  
Author(s):  
Elżbieta Antczak
Keyword(s):  
Spatial Data ◽  
Spatial Dependence ◽  
Regression Models ◽  
Seemingly Unrelated Regression ◽  
Spatial Data Analysis ◽  
Spatial Dependency ◽  
Empirical Examination ◽  
Spatial Panel ◽  
Spatial Weights ◽  
Unrelated Regression

This paper investigates how to determine the values (elements) of spatial weights in a spatial matrix (W) endogenously from the data. To achieve this goal, geostatistical tools (standard deviation ellipsis, semivariograms, semivariogram clouds, and surface trend models) were used. Then, in the econometric part of the analysis, the effect of applying different variants of matrices was examined. The study was conducted on a sample of 279 Polish towns from 2005–2015. Variables were related to the quantity of produced waste and economic development. Both exploratory spatial data analysis and estimations of spatial panel and seemingly unrelated regression models were performed by including particular W matrices in the study (exogenous-random as well as distance and directional matrices constructed based on data). The results indicated that (1) geostatistical tools can be effectively used to build Ws; (2) outcomes of applying different matrices did not exclude but supplemented one another, although the differences were significant; (3) the most precise picture of spatial dependence was achieved by including distance matrices; and (4) the values of the assessed parameter at the regressors did not significantly change, although there was a change in the strength of the spatial dependency.

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