Bayesian Estimation of Partially Linear Additive Spatial Lag Quantile Regression Models with Free-Knot Splines
At present,the research of partial linear additive spatial lag models is almost based on the estimation of mean regression.However,mean regression studies the influence of covariates on the mean position of response variables in conditional distribution,which can't reflect the relationship between them in the tail of condi-tional distribution,which is easy to cause the omission of information.In order to overcome this defect,this paper constructs a partial linear additive spatial lag quantile regression model(PLASLQRM).On the basis of fitting nonparametric functions with free-knot splines,Bayesian estimation is carried out with the help of reversible jump Markov chain Monte Carlo algorithm,and a Bayesian quantile regression method(BFQ)based on free-knot splines is formed.In order to test the effectiveness of BFQ method,this method is simulated and compared with Bayesian quantile regression method based on P-splines(BPQ),Bayesian mean regression method based on free-knot splines(BFM)and generalized moment method(GMM).The results show that compared with the other three methods,BFQ method is less vulnerable to extreme values and has more stable performance.Furthermore,when the error distribution is characterized by sharp peak,thick tail and skew,this method has more advantages in the estimation of parametric part and the fitting of nonparametric part.Finally,the provincial carbon emission is selected as the empirical research object,and the influence of various factors on its linearity and nonlinearity is analyzed by using BFQ method,which further verifies the ability of this method to estimate parametric and nonparametric functions in practical problem.
partially linear additive spatial lag modelquantile regressionBayesian estimationfree-knot splines
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