Change-plane analysis in functional response quantile regression

Change-plane analysis is a pivotal tool for identifying subgroups within a heterogeneous population, yet it presents challenges when applied to functional data. In this paper, we consider a change-plane model within the framework of functional response quantile regression, capable of identifying and testing subgroups in non-Gaussian functional responses with scalar predictors. The proposed model naturally extends the change-plane method to account for the heterogeneity in functional data. To detect the existence of subgroups, we develop a weighted average of the squared score test statistic, which has a closed form and thereby reduces the computational stress. An alternating direction method of multipliers algorithm is formulated to estimate the functional coefficients and the grouping parameters. We establish the asymptotic theory for the estimates based on the reproducing kernel Hilbert space and derive the asymptotic distributions of the proposed test statistic under both null and alternative hypotheses. Simulation studies are conducted to evaluate the performance of the proposed approach in subgroup identification and hypothesis test. The proposed methods are also applied to two datasets, one from a study on China stocks and another from the COVID-19 pandemic.