Research On Adaptive LASSO Method In Spatial Regression Models Under Fixed-Effect Conditions

Panel data refers to data that contains multiple individuals,and the same individual has a series of different time observations,including two dimensions: section dimension and time dimension.To consider the relationship between data in geographic observations,spatial econometrics is required to deal with the spatial correlation and spatial heterogeneity of data.For the spatial panel data,it is affected by time and individual factors as well as spatial factors,and the amount of information contained is larger and the structure is more complex.The spatial panel data model comprehensively considers the above factors and has a good application prospect.The higher the data dimension,the greater the amount of information.But a high dimension is not necessarily good.In order to overcome the dimensionality disaster,obtain the essential characteristics of data,and remove useless data,dimensionality reduction is imperative.LASSO(Least absolute shrinkage and selection operator)method can select parameters through parameter reduction,which can achieve the purpose of dimensionality reduction,and is often applied to model improvement and selection.The adaptive LASSO method inherits the excellent properties of the LASSO method and overcomes the shortcomings of variable selection inconsistency of the LASSO method,and has become a widely used method.In this paper,the variable selection problem of fixed-effect spatial regression model is studied,and the adaptive LASSO method is used to perform model selection and parameter estimation at the same time,and it is proved that when the adaptive LASSO method is used to properly select the tuning parameters and use the consistent estimate with appropriate convergence velocity as the initial estimate,the estimated quantities obtained have consistency,asymptotic normality and good Oracle properties.The application of adaptive LASSO method can significantly reduce the computational burden without sacrificing asymptotic efficiency.The main content of this article is divided into two chapters:The first chapter is an introduction,which briefly introduces the research background and significance of the problem,the research overview of the spatial panel data model and variable selection method,and the content and structure of this paper.The second chapter briefly introduces the spatial panel data model and its related knowledge,transforms the fixed-effect spatial regression model studied in this paper,and uses the adaptive LASSO method to study.Given the hypothesis,two theorems are proved.The Monte Carlo method was applied for simulation,and the excellent properties of the adaptive LASSO method were verified by the results of Monte Carlo simulation.The innovation of this paper: In the fixed-effect space panel data model,the Adaptive LASSO penalty function is constructed to study the variable selection problem of the spatial panel data model.The Adaptive LASSO method allows simultaneous model selection and parameter estimation.To a certain extent,the properties of the LASSO method are improved and the operability is better.