Empirical Likelihood Inference Of Spatial Panel Data Model With Time Varying Coefficients

With the rapid development of big data,people can get a lot of data from the computer.When dealing with data,if we only consider the temporal or spatial differences of the data,it will often make the data lose a lot of its own meaning.The data generated by human activities or other economic behaviors are often affected by time,space or other factors.Due to the existence of spatial correlation,the data often obtained are not independent.However,in the traditional statistical methods,it is necessary to meet the basic assumption of sample independence,so it is necessary to study new methods to deal with spatial data.Spatial econometrics is also widely concerned.Compared with the traditional spatial econometric model,spatial panel data model takes spatial correlation and spatial heterogeneity into account,so the parameter estimation of spatial panel data model is more effective than the traditional spatial econometric model.Nowadays,spatial econometrics has become a hot spot,and time-varying coefficient spatial panel data model can more comprehensively consider the spatial heterogeneity.Since Owen proposed the empirical likelihood method,it has attracted the attention of many scholars with its unique advantages.The empirical likelihood method can estimate the population distribution directly through the data when the population distribution is unknown,it has a sampling characteristic similar to bootstrap.The confidence interval constructed by empirical likelihood method has domain retention and transformation invariance.The shape of confidence region is determined by data itself,which makes the empirical likelihood method widely used in various statistical models.At present,there are few applications of empirical likelihood method in spatial panel data model.The existing theoretical research mainly focuses on the generalized moment estimation,maximum likelihood estimation and quasi maximum likelihood estimation of spatial panel data model.The research on empirical likelihood estimation is relatively less,It has a certain research significance for the inference of time-varying coefficient spatial panel data model.In this paper,the empirical likelihood inference of spatial panel data model with time-varying coefficients is studied.By using martingale difference sequence,the quadratic form of the estimation equation is transformed into linear form,and the empirical likelihood ratio statistics of model parameters are constructed.It is proved that the limit distribution of the statistics obeys chi square distribution under certain conditions.Finally,the main conclusions of this paper are verified by random simulation.