Variable selection in high-dimensional varying coefficient panel data models with fixed effects

Abstract

To address the challenges of variable selection in panel data models with fixed effects and varying coefficients, we introduce a novel method that combines basis function approximations with group nonconcave penalty functions. By utilizing a forward orthogonal deviation transformation, we eliminate fixed effects, allowing us to select significant variables and estimate non-zero coefficient functions. Under certain regularity conditions, we demonstrate that our method consistently identifies the true model structure, and the resulting estimators exhibit oracle properties. For computational efficiency, we have developed a group gradient descent algorithm that incorporates a transformation of the penalty terms. Simulation studies reveal that nonconvex penalties (SCAD/MCP) outperform the Lasso across various performance metrics. Furthermore, compared to existing methods, our approach significantly reduces false positives (FPs). To demonstrate the practical applicability and effectiveness of our method, we present an analysis of a real dataset.