Variable selection for semiparametric varying-coefficient spatial autoregressive models with a diverging number of parameters

Abstract

In this article, we consider variable selection in semiparametric varying-coefficient spatial autoregressive models with a diverging number of parameters. With the nonparametric functions approximated by B-spline basis functions and combining 2SLS method with the SCAD penalty, we propose a variable selection procedure. Under mild conditions, we establish the consistency and oracle property of the resulting estimators for parameter components and consistency of the regularized estimator for nonparametric component. Some simulation studies are conducted to assess the finite sample performance of the proposed variable selection procedure, and the developed methodology is illustrated by an analysis of the Boston housing price data.

Keywords:

• Semiparametric varying-coefficient
• spatial autoregressive
• variable selection
• instrumental variable

Acknowledgments

The authors thank two anonymous referees and the editor in chief for their constructive comments that resulted in an improved manuscript.

Additional information

Funding

This research was supported by the International Research Cooperation Seed Fund of Beijing University of Technology (2018B34) and National Natural Science Foundation of China (11471036).