Local Walsh-average regression for spatial autoregression single index varying coefficient models

In real life, a large number of variables are spatially correlated in adjacent regions in various fields, such as finance, sociology, ecology, and geographic information systems. And the factors affecting these variables often have both linear and non linear relationships with them, how to accurately depict the relationship between them with a spatial regression model is a significant work. In order to further accurately describe the relationship between explanatory variables and response variables, we establish a spatial autoregressive single index varying coefficient model. The least squares method is the main method of model estimation but it is not robust enough when the parameter distribution is not normal. We present a new estimation method based on local Walsh average-regression. Under some general assumptions, we establish the asymptotic properties of the parametric and non parametric estimators. We further verify the accuracy and efficiency of the estimators under the condition of non normal error distribution through numerical experiments. In addition, the robustness of the proposed method is verified when the spatial weight matrix is interfered and when the bandwidth is changed within a certain range. Finally, we demonstrate the accuracy of forecasting by our proposed model compared with traditional spatial autoregressive model through real data analysis.