Subgroup learning in functional regression models under the RKHS framework

Motivated by the inherent heterogeneity observed in many functional or imaging datasets, this paper focuses on subgroup learning in functional or image responses. While change-plane analysis has demonstrated empirical success in practice, the existing methodology is confined to scalar or longitudinal data. In this paper, we propose a novel framework for estimation, identifying, and testing the existence of subgroups in the functional or image response through the change-plane method. The asymptotic theories of the functional parameters are established based on the vector-valued Reproducing Kernel Hilbert Space (RKHS), and the asymptotic properties of the change-plane estimators are derived by a smoothing method since the objective function is nonconvex concerning the change-plane. A novel test statistic is proposed for testing the existence of subgroups, and its asymptotic properties are established under both the null hypothesis and local alternative hypotheses. Numerical studies have been conducted to elucidate the finite-sample performance of the proposed estimation and testing algorithms. Furthermore, an empirical application to the COVID-19 dataset is presented for comprehensive illustration.