This paper develops an efficient variable selection method for semi-parametric varying coefficient spatial error models (SVCSEM) by integrating profile likelihood with adaptive LASSO penalization. The proposed method performs variable selection and model estimation simultaneously for the SVCSEM. The asymptotic normality and selection consistency of the resulting estimators are established under mild regularity conditions. Extensive numerical simulations demonstrate that the proposed method identifies the true effects accurately while delivering precise estimation for both parametric and nonparametric components under finite samples. Notably, simulation results highlight the superior performance of the adaptive LASSO, which consistently outperforms both the standard LASSO and the smoothly clipped absolute deviation (SCAD) penalty in terms of selection accuracy and estimation efficiency in the SVCSEM framework. In the analysis of China's outward foreign direct investment (OFDI) across 51 Belt and Road Initiative (BRI) countries, our findings reveal that institutional quality exerts significant nonlinear moderating effects on the relationship between gross domestic product (GDP) and OFDI, while also identifying the key determinants of investment. Further robustness analyses confirm the reliability of our methodology under alternative specifications of spatial weight matrices, affirming its broad applicability and effectiveness in empirical research.
Citation: Yu Liu, Zengchao Xu. Variable selection for semi-parametric varying coefficient spatial error models[J]. AIMS Mathematics, 2026, 11(4): 10133-10158. doi: 10.3934/math.2026418
This paper develops an efficient variable selection method for semi-parametric varying coefficient spatial error models (SVCSEM) by integrating profile likelihood with adaptive LASSO penalization. The proposed method performs variable selection and model estimation simultaneously for the SVCSEM. The asymptotic normality and selection consistency of the resulting estimators are established under mild regularity conditions. Extensive numerical simulations demonstrate that the proposed method identifies the true effects accurately while delivering precise estimation for both parametric and nonparametric components under finite samples. Notably, simulation results highlight the superior performance of the adaptive LASSO, which consistently outperforms both the standard LASSO and the smoothly clipped absolute deviation (SCAD) penalty in terms of selection accuracy and estimation efficiency in the SVCSEM framework. In the analysis of China's outward foreign direct investment (OFDI) across 51 Belt and Road Initiative (BRI) countries, our findings reveal that institutional quality exerts significant nonlinear moderating effects on the relationship between gross domestic product (GDP) and OFDI, while also identifying the key determinants of investment. Further robustness analyses confirm the reliability of our methodology under alternative specifications of spatial weight matrices, affirming its broad applicability and effectiveness in empirical research.
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Yu Liu, Zengchao Xu. Variable selection for semi-parametric varying coefficient spatial error models[J]. AIMS Mathematics, 2026, 11(4): 10133-10158. doi: 10.3934/math.2026418
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