基于贝叶斯估计的空间函数型自回归模型及其应用

Spatial Function Autoregressive Model Based on Bayesian Estimation and Its Application

目的为了研究函数型数据中响应变量的空间相关性,根据现有研究方法,对具有空间依赖性的函数型数据进行研究,并提出其模型的贝叶斯估计方法。方法以典型空间自回归模型为基础,根据函数响应变量的空间依赖性,假设响应变量和解释变量间存在内生关系,生成空间函数型自回归模型,通过主成分分析将模型中函数型部分变为离散型,然后在给定先验情况下计算模型中参数的完全条件后验分布,使用贝叶斯MCMC方法进行估计。结果使用联合Gibbs采样和随机游动的Metropolis-Hastings算法对模型中参数进行估计,通过模拟研究发现:不同参数下模型的函数型系数以及其他参数的估计偏差和均方误差较小,由此验证了贝叶斯估计方法的有效性,同时将空间函数型模型用于重庆市主城区新房平均价格的实证分析,结果表明所提出模型的贝叶斯估计方法是有效的。结论使用贝叶斯估计方法对模型中参数进行估计,在不同情况下函数型解释变量的估计效果一直都比较好,并且随着样本量的增大,其估计效果也越来越好,可以认为使用贝叶斯估计方法对空间函数型自回归模型进行估计是有效且可行的,同时通过实证分析说明重庆市主城区新房平均价格具有空间自相关性,而且会受到二手房挂牌量的影响。

Objective To study the spatial correlation of response variables in functional data,according to existing research methods,functional data with spatial dependence were studied and the Bayesian estimation method was proposed.Methods Based on the typical spatial autoregressive model and according to the spatial dependence of the functional response variables,the spatial function autoregressive model was generated by assuming that there was an endogenous relationship between the response variables and the explanatory variables.The functional components in the model were changed into discrete types by the principal component analysis,and then the complete conditional posterior distribution of the parameters in the calculation model was calculated under a given prior condition.The parameters in the model were estimated using the Bayesian MCMC method.Results The Metropolis-Hastings algorithm,which combined Gibbs sampling and random walk,was used to estimate the parameters in the model.Through simulation research,it was found that the functional coefficients of the model and the estimation deviations and mean square errors of other parameters under different parameter models were small,which verified the effectiveness of the Bayesian estimation method.At the same time,the spatial function model was applied to the empirical analysis of the average price of new houses in the main urban area of Chongqing.The results show that the Bayesian estimation method of the proposed model is effective.Conclusion The estimation effect of functional explanatory variables using Bayesian estimation method to estimate the parameters in the model is always better under different circumstances,and its estimation effect is also more and more effective as the sample size increases.Thus,it can be considered that using spatial function model to estimate the spatial function autoregressive model is effective and feasible.Meanwhile,the empirical analysis shows that the average house price of new houses in the main urban area of Chongqing has spatial autocorrelation,and it will be affected by the listing volume of second-hand houses.