Estimation Of Semi-Parametric Spatial Autoregressive Models With Randomly Missing Data

Spatial data are very common in epidemiological surveillance,geographical statistics,air quality monitoring,oceanography and econometrics.Because there is usually spatial dependence of spatial data,the traditional regression models are challenged,the spatial models emerged as the times require.Among all of spatial models,the spatial autoregressive model has been extensively studied.However,although the spatial autoregressive model has good interpretability,it is easy to cause large model bias when the model is misspecified.Therefore,some scholars introduced the nonparametric function into the model and proposed semi-parametric spatial autoregressive models.The research results of semi-parametric spatial autoregressive models are mainly focused on complete data,but missing data often occur in actual data analysis.For example,some patients gave up treatment in drug efficacy study because of the side effects of drugs,which resulted in data missing.Therefore,it is of theoretical and practical significance to study the missing data problem of semi-parametric spatial autoregressive models.In this paper,the estimation of the semi-parametric spatial autoregressive model with randomly missing data in the response variable was mainly studied.Firstly,the model was estimated by regression imputation and two-stage least squares method,and then the asymptotic properties of estimation were proved.Finally,the two-stage least squares estimations based on regression imputation were compared with different missing ratios.The results showed that the two-stage least squares estimation based on regression imputation could effectively improve the estimation effect of the model compared with the estimation based on incomplete data.