Subgroup analysis for high-dimensional functional regression

Xiaochen Zhang, Qingzhao Zhang, Shuangge Ma, Kuangnan Fang

Abstract: Subgroup analysis for scalar data has been well studied in the literature. However, less has been done on functional data, especially on high-dimensional functional regression. In this study, we develop a high-dimensional functional regression model for simultaneous estimation and subgroup identification for a heterogeneous population. Under mild conditions, we establish the estimation and selection consistency of the proposed estimators. The proposed analysis allows the number of functional predictors and number of subgroups to increase as the sample size increases. Simulation studies demonstrate satisfactory performance of the proposed method, and it is also illustrated through a real application.