Empirical Likelihood For Matrix Exponential Spatial Specification

As a wide range of research fields,spatial econometrics has become the focus of many scholars such as economics and statistics.With the rapid development of economy and society,the relevant theories and application achievements of spatial econometrics are increasingly rich,including the basic theories,model setting,parameter estimation and hypothesis testing of various spatial econometric models.Spatial autoregression model(SAR model)is the spatial econometrics,the most basic and the most classic model,SAR and its derived model estimation problem has been at the core of academic research,more common model parameter estimation method has maximum likelihood estimation,quasi-maximum likelihood estimation,two-stage least squares estimation and generalized moment estimation method.The Empirical likelihood method is a non-parametric statistical inference method under full samples proposed by Owen,which maximizes the parametric likelihood ratio function under certain constraints,which has sampling properties similar to Bootstrap.The empirical likelihood method has the advantages of domain retention,transformation invariance,the shape of the confidence interval is determined by the data itself,Bartlett correction and no construction axis statistics.These advantages enable the empirical likelihood approach in many statistical models.In recent years,some scholars have applied the empirical likelihood method in the nonparametric statistical inference method to the estimation problems of spatial autoregression and other common spatial econometric models,and have obtained many excellent research results.Le Sage and Pace proposed that the Matrix Exponential Spatial Specification(MESS)can be used to describe the spatial correlation.The matrix index can replace the spatial autoregressive process,but the two cannot be nested with each other.In essence,the exponential decay of spatial autoregression replaces the geometric exponential decay.Compared with the conventional spatial autoregressive models,the MESS model has significant advantages in both theoretical modeling,computation,and interpretation.As an alternative to the traditional SAR model,the theoretical generalization of the MESS model deserves further discussion.Scholars' research on the parameter estimation problem of MESS models mainly focuses on quasi-maximum likelihood estimation and generalized moment estimation methods,but the literature applying empirical likelihood methods to MESS models has not seen the public research results reported.Therefore,this paper studies the empirical likelihood inference of matrix exponential spatial econometric models with some theoretical value and expands the statistical inference methods of MESS models.The main research work of this paper can be summarized as the following two points:First,on the basis of the existing theoretical research,this paper studies the empirical likelihood inference of the MESS truncation data model with spatial autoregression error,transforms the quadratic type in the estimation equation into a linear form,constructs the empirical likelihood ratio statistics of the model parameters,and constructs the confidence interval of the model parameters.Second,the MESS truncated data model is further extended to MESS panel data model,study the empirical likelihood inference of MESS panel data model with fixed effects,using the martingale difference sequence quadratic equation into linear form,construct the empirical likelihood ratio statistics of model parameters,under certain conditions,the limit distribution of empirical likelihood ratio statistics is chi-square distribution,and study the good quality of these confidence intervals through numerical simulation.