Sparse functional linear models via calibrated concave-convex procedure

In this paper, we propose a calibrated ConCave-Convex Procedure (CCCP) for variable selection in high-dimensional functional linear models. The calibrated CCCP approach for the Smoothly Clipped Absolute Deviation (SCAD) penalty is known to produce a consistent solution path with probability converging to one in linear models. We incorporate the SCAD penalty into function-on-scalar regression models and phrase them as a type of group-penalized estimation using a basis expansion approach. We then implement the calibrated CCCP method to solve the nonconvex group-penalized problem. For the tuning procedure, we use the Extended Bayesian Information Criterion (EBIC) to ensure consistency in high-dimensional settings. In simulation studies, we compare the performance of the proposed method with two existing convex-penalized estimators in terms of variable selection consistency and prediction accuracy. Lastly, we apply the method to the gene expression dataset for sparsely estimating the time-varying effects of transcription factors on the regulation of yeast cell cycle genes.