Spline Estimation In Functional Spatial Autoregressive Model

With the rapid development of information technology,more and more real-time data are collected.This kind of data is called functional data because of its high dimension and continuity.Functional data widely exist in various fields of society,and the analysis of functional data has become more and more popular in statistical analysis.Another kind of spatial data,considering the effect of spatial dependence,is also a hot topic for scholars to analyze the data under the spatial dimension.Therefore,it is of great social adaptability and necessity to consider the spatial model under the functional data.In this paper,the spline estimation problem of functional spatial autoregressive model is considered.The maximum likelihood estimation method is used to estimate the initial values and slope functions of different parameters.Furthermore,considering the existing functional principal component analysis method,the estimation results of the two methods are evaluated and compared.Through R software programming.The results show that both b-spline method and functional principal component analysis method can achieve good results in simulated estimation of functional data,and with the increase of sample size,the better the estimation effect of parameters is,the better the fitting effect of slope function is,and the fitting curve of slope function under b-spline method is smoother.The corresponding empirical analysis shows that the error of considering the spatial effect is smaller and the effect is better.