Estimation And Properties Of Variable Coefficient Spatial Autoregressive Models

Since the beginning of 1990 s,the model with spatial structure has been put forward and attracted the attention of the majority of statisticians at home and abroad.Nowadays,with the deepening of research problems,the variable coefficient space autoregressive model has become the research goal of many scholars at home and abroad.In the 1960 s,people put forward the variable selection method to deal with the data and obtain the optimal data information when the amount of observation data is too large.As many variable selection methods have been put forward one after another,the topic of variable selection is still one of the hot topics in modern statistical analysis.At present,there are relatively few achievements in the research on the variable coefficient spatial autoregressive model,especially in the research on the combination of variable coefficient spatial autoregressive model and variable selection.Based on the existing theories of the two,this paper mainly studies the following two issues:（1）Under the maximum likelihood criterion,the parameter estimation of spatial lag coefficient in variable coefficient spatial autoregressive model is discussed.The covariate coefficients are approximated by the -spline basis function,and the variable coefficient problem is transformed into a ”linear” model problem;Secondly,the cross-sectional maximum likelihood method is used to find the parameter estimation of the spatial lag coefficient;Under some basic assumptions,the consistency of spatial lag coefficient is proved;The properties of finite samples are studied by numerical simulation with statistical software;Application of Boston house price data to explore case analysis.（2）Based on the theory and method of variable selection,the transformed variable coefficient model was used for unified variable selection by standard B-spline basis function approximation and twice adaptive-Lasso variable selection method,so as to realize the purpose of separating the influence modes in the model.The asymptotic normality of constant coefficient estimation and the approximate speed of variable coefficient function estimation in the model are proved under the premise of giving the basic assumption.Numerical simulation is carried out to study the properties of limited samples,and applied to the analysis of Boston case data,and the results are consistent with the existing conclusions.