The Estimation And Test Of Spatial Single-index Autoregressive Model

As a new subject of branch of econometrics,Spatial econometrics develops quickly and more and more scholars discuss its theory and application in deep.The basis of Spatial e-conometrics is Spatial autoregressive model and this model become applied to build model in wide range.But Spatial autoregressive model is a parametric model and the parametric model can’t well explain the actual data under the actual data generation mechanism.So in order to better explore the complex relationship between the variables,nonparametric and semiparametric model in the field of econometrics and statistics have been seriously treated,however,the results of the study that is analysising spatial data based on nonpara-metric and semiparametric model are relatively less.In order to better explain the data and avoid the "curse of dimensionality",Firstly,we come up with the Spatial single-index autoregressive model,Spatial single-index autore-gressive model is improved model of parametric Spatial autoregressive model and semi-parametric single-index regressive model,because it not only has the unique characteristics of dimension reduction but also can be better fitting spatial data,the study will be a very meaningful things.Secondly,since the local linear is a better way to approximate unknown functions and M-type estimate is a more robust estimation method,we use the two-step local linear smoothing methods combined with M-type estimate methods and Maximum Likelihood Estimation to estimate the spatial single-index autoregressive model,then test the parametric and nonparametric part of this model based on Bootstrap.Finally,we test the effectiveness of the method through the numerical simulation.