Subgroup analysis for the functional linear model

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.

Automated summary

This paper extends the classical functional linear regression model to allow for heterogeneous coefficient functions among different subgroups of subjects. A penalization-based approach is proposed to simultaneously determine the number and structure of subgroups and coefficient functions within each subgroup. The paper provides an effective computational algorithm and establishes the oracle properties and estimation consistency of the model. Extensive numerical simulations demonstrate its superiority compared to competing methods, and an analysis of an air quality dataset leads to interesting findings and improved predictions.