Automatic variable selection for semiparametric spatial autoregressive model

Abstract

This article studies the generalized method of moment estimation of semiparametric varying coefficient partially linear spatial autoregressive model. The technique of profile least squares is employed and all estimators have explicit formulas which are computationally convenient. We derive the limiting distributions of the proposed estimators for both parametric and non parametric components. Variable selection procedures based on smooth-threshold estimating equations are proposed to automatically eliminate irrelevant parameters and zero varying coefficient functions. Compared to the alternative approaches based on shrinkage penalty, the new method is easily implemented. Oracle properties of the resulting estimators are established. Large amounts of Monte Carlo simulations confirm our theories and demonstrate that the estimators perform reasonably well in finite samples. We also apply the novel methods to an empirical data analysis.

Keywords:

• Asymptotic properties
• automatic variable selection
• generalized method of moments
• semiparametric spatial autoregressive model
• smooth-threshold estimating equation

JEL Classification:

• C13
• C14
• C21

Acknowledgment(s)

The authors are grateful to the Editor Esfandiar Maasoumi, an associate editor and the anonymous referees for their valuable comments which enhanced quality of the paper very much.

Disclosure statement

No potential conflict of interest was reported by the authors.

Data availability statement

The Boston housing price data with its detailed descriptions is freely available from the package spdep of software R.

Additional information

Funding

Jing Yang’s research was supported by the Natural Science Foundation of Hunan Province (Grant 2022JJ30368), the Scientific Research Fund of Hunan Provincial Education Department (Grant 22A0040) and the National Natural Science Foundation of China (Grants 11801168, 12071124). Xuewen Lu’s research was supported by the Discovery Grant (RG/PIN06466-2018) from Natural Sciences and Engineering Research Council of Canada.