| With the vigorous development of science and technology in recent years,the means of data collection are becoming more and more abundant.Compared with the previously discrete observed data points,more real-time data on continuous indicators are collected and recorded.This kind of functional data with continuity and high-dimensional characteristics is widely used in many fields.The functional data analysis method that came into being has also become the focus of current scientific research.Regression analysis is a very important research content in functional data analysis,but the existing studies usually assume that the data are time-dependent or independent,but in some cases,these assumptions may not be reasonable,such as the data between different regions may have spatial dependence.Therefore,this dissertation studies the estimation and test of Functional Partial Linear model in the case of spatial dependence,it has certain theoretical significance and practical application value.Specifically,the main research contents of this paper are as follows:This dissertation describes the regression between scalar response variables with spatial dependence structure and functional covariates,adds the general linear part,and proposes a new functional partial linear spatial autoregressive model(FPLSARM).The parameters in the model are estimated by B-spline method and quasi maximum likelihood estimation(QMLE).Under certain regular conditions,the asymptotic properties of parameter estimation are obtained.Further,in order to verify whether the regression coefficients of the parameter part of the model meet certain linear constraints,a method based on residual bootstrap test is proposed.Finally,the effectiveness of the estimation and test method is verified through simulation research and real data analysis.The results show that with the continuous increase of sample size,The deviation and error of parameter estimation are decreasing,the test statistics also have good level and efficacy,and the model also achieves good fitting on the real data. |
