Panel data offers valuable insights into both temporal and cross-sectional variations, making it essential for analyzing complex problems. To address dimensionality reduction challenges in high-dimensional varying coefficient panel data models with fixed effects, we propose a novel variable selection method that combines basis function approximation with non-convex group penalties (SCAD/MCP). Using auxiliary regression and orthogonal projection, we isolate fixed effects to prevent their interference in variable selection. Basis function expansion approximates nonlinear coefficients, enabling simultaneous identification of the true model structure and estimation of non-zero coefficients. Under some regularity conditions, our method consistently identifies the true model, with the estimator exhibiting the oracle property. We employ a group descent algorithm to solve the penalized objective function. Simulation studies demonstrate that SCAD and MCP outperform Lasso in variable selection accuracy, reducing false positives and enhancing coefficient estimation. When applied to real data, our method effectively identifies important variables and delivers superior predictive performance.
Yang et al. (Thu,) studied this question.