Research On Robust Model Identification Of Spatial Varying Coefficient Quantile Regression Model

The spatial varying coefficient regression model has received widespread attention due to its excellent characteristics in spatial data analysis.The main feature is that this model can handle the problem of spatial non-stationarity.Quantile regression method is robust to non-normally distributed data or outliers in response variables,but it cannot handle situations where covariates have outliers.In addition,many noisy/irrelevant variables are often included in the high-dimensional data analysis.How to accurately find these unrelated or low-correlation variables to improve the interpretability of the model is very necessary.Even some variables are related to response variables,this correlation probably not change with the time or space,thus it is also make sense to identify those constant coefficient variables in order to improve the simplicity of the model.For these reasons,this paper aims to study the robust model identification problem of the spatial varying coefficient regression model by combining the weighted quantile method and the idea of double-shrinkage approach.The proposed method can effectively handle the non-normally distributed errors and the outliers involved in either the response variable or the covariates or both of them.Finally,the robustness and effectiveness of the new method are demonstrated by some Monte Carlo simulations and a real data analysis.