Variable Selection for Panel Data Linear Regression Models with Fixed Effects

This paper introduces a robust variable selection mechanism for fixed effect panel data models by integrating compound quantile regression with the adjusted MIXED penalty method. Initially, forward orthogonal deviation transformation is employed to eliminate the influence of fixed effects. Subsequently, the MIXED penalty is utilized to construct a penalized compound quantile regression objective function, facilitating simultaneous estimation of regression coefficients and variable selection. This method not only effectively eliminates the interference of fixed effects but also demonstrates outstanding robustness. Its performance with limited sample sizes was validated through simulation studies, and its practical value was illustrated through application in real data analysis.