部分线性可加空间滞后分位数回归模型的贝叶斯估计——基于自由节点样条的研究

Bayesian Estimation of Partially Linear Additive Spatial Lag Quantile Regression Models with Free-Knot Splines

部分线性可加空间滞后模型的研究目前几乎都建立在均值回归的估计之上.均值回归研究协变量对响应变量在条件分布均值位置的影响,并不能反映两者在条件分布尾部的关系,容易造成信息的遗漏.为了克服这一缺陷,本文构建了部分线性可加空间滞后分位数回归模型(PLASLQRM),在采用自由节点样条拟合非参数函数的基础上,借助逆跳马尔可夫链蒙特卡罗算法对其进行了贝叶斯估计,形成了基于自由节点样条的贝叶斯分位数回归方法(BFQ).为检验BFQ方法的有效性,将该方法与基于惩罚样条的贝叶斯分位数回归方法(BPQ),基于自由节点样条的贝叶斯均值回归方法(BFM)和广义矩方法(GMM)进行了模拟比较.结果显示,BFQ方法与其它三种方法相比更不易受异常值的影响,性能更稳定.并且,在误差分布呈尖峰厚尾和偏斜特征时,该方法对参数部分的估计和非参数部分的拟合都更具优势.最后,选取省域碳排放量为实证研究对象,运用BFQ方法分析各类因素对其线性和非线性的影响,进一步验证了该方法在实际问题中估计参数和非参数的能力.

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 conditional 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 freeknot 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.