Regression Parameter Estimation In The System Of Seemingly Unrelated Regressions

Regression model is widely used in economics,mathematics,computer science,engineering and other fields.Domestic and foreign scholars have done a lot of research on this kind of model,among which the estimation of regression parameter is one of the important research fields.Among many regression models,seemingly unrelated regres-sion model and constrainted regression model play an important role and have a wide range of application scenarios.Mixed model is a kind of widely used model,which is often used to fit complex data.In this paper,we study the regression parameter esti-mation problem in the system of seemingly unrelated regressions with linear constraint and the system of seemingly unrelated mixed model.The system of seemingly unrelated regressions with linear constrainthas has both the unrelated information in seemingly unrelated regression model and the constraint conditions in constrainted regression model.The main content contains:We intro-duce the covariance-adjusted constraint estimator and the constrainted covariance ad-justment estimator,and prove that they are unbiased and optimal than the constraint-ed least squares estimator and the covariance adjustment estimator,respectively.If ?is unknown,we define the two-stage covariance-adjusted constraint estimator and the two-stage constrainted covariance adjustment estimator,and discuss their superiorities by theoretical demonstration and numerical simulations.Employing the matrix power series,we obtain the estimator of regression parameter in the system of two seemingly unrelated regressions with liner constraint,and further compare it with the limit of the sequence of the covariance-adjusted constraint estimator and the limit of the sequence of the constrainted covariance adjustment estimator.For two important cases,we exhib-it some interesting relationships between the limit of the covariance-adjusted constraint estimator sequence and the limit of the constrainted covariance adjustment estimator sequence.Finally,we extend seemingly unrelated regression model to the seemingly unrelat-ed mixed model and study the regression parameter estimation problem.The main content contains:If the covariance is known,we introduce the covariance-adjusted generalized least square estimation and prove that it is unbiased and better than the generalized least square estimation.If the covariance is unknown,we define two-step covariance-adjusted least squares estimation and discuss its superiorities by numerical simulations.