Subgroup analysis for the functional linear model

• Published in: Journal of statistical planning and inference Vol. 231; p. 106120
• Main Authors: Sun, Yifan, Liu, Ziyi, Wang, Wu
• Format: Journal Article
• Language: English
• Published: Elsevier B.V 01.07.2024
• Subjects: ADMM algorithm; B-spline basis; Functional linear regression; Minimax concave penalty; Subgroup analysis; Subgroup analysis; B-spline basis; Minimax concave penalty; Functional linear regression; ADMM algorithm
• ISSN: 0378-3758; 1873-1171
• DOI: 10.1016/j.jspi.2023.106120

Classical functional linear regression models the relationship between a scalar response and a functional covariate, where the coefficient function is assumed to be identical for all subjects. In this paper, the classical model is extended to allow heterogeneous coefficient functions across different subgroups of subjects. The greatest challenge is that the subgroup structure is usually unknown to us. To this end, we develop a penalization-based approach which innovatively applies the penalized fusion technique to simultaneously determine the number and structure of subgroups and coefficient functions within each subgroup. An effective computational algorithm is derived. We also establish the oracle properties and estimation consistency. Extensive numerical simulations demonstrate its superiority compared to several competing methods. The analysis of an air quality dataset leads to interesting findings and improved predictions. •Pairwise-penalization-based approach to determine the coefficient functions.•Oracle properties and estimation consistency of the proposed approach are built.•Great performance in numerical simulation and real data analysis.