A more accurate estimation with kernel machine for nonparametric spatial lag models

Abstract

Ignoring potential spatial autocorrelation in georeferenced data may cause biased estimators. Furthermore, existing studies assume insufficiently flexible structure of spatial lag model for some practical applications, which makes it difficult to portray the complex relationship between responses and covariates. Thus, we propose a novel garrotized kernel machine estimation method for the nonparametric spatial lag model and develop an eigenvector spatial filtering algorithm with sparse regression to filter spatial autocorrelation out of the residuals. The “one-group-at-a-time” cyclical coordinate descent algorithm is introduced for a solution path of tuning parameters. Our method can better describe the potential nonlinear relationship between responses and covariates, making it possible to model high-order interaction effects among covariates. Numerical results and the analysis of commodity residential house prices in large and medium-sized Chinese cities indicate that the proposed method achieves better prediction performance compared with competing ones. The result of real data analysis can provide guidance for the government to take targeted suppression measures of house prices for different areas.