A1985
Title: Joint structural break detection and variable selection in high-dimensional functional models: Sleep EEG application
Authors: Mengfei Ran - Xi\'an Jiaotong-Liverpool University (China) [presenting]
Abstract: Disentangling localized structural regime shifts from smooth time-varying covariate effects in ultra-high-dimensional functional data $(p \gg n)$ remains a fundamental statistical challenge. Standard functional data analysis (FDA) methods, which predominantly prioritize smoothness, are fundamentally ill-equipped to simultaneously perform variable selection and identify abrupt structural changepoints. To bridge this gap, Adaptive Joint Learning (AJL) is introduced, a hierarchical regularization framework designed to jointly identify active functional predictors and detect shared structural changepoints in multivariate time-varying models. Distinct from conventional simultaneous estimation, a theoretically grounded two-stage screening-and-refinement procedure is proposed. Theoretically, by employing a Primal-Dual Witness construction and enforcing a formalized undersmoothing condition, the AJL estimator achieves consistent support recovery, accurate changepoint localization, and asymptotic normality for valid inference, even under high design correlation. To demonstrate its practical utility, the proposed framework is applied to the Sleep-EDF database. AJL successfully identifies a synchronized structural break marking the NREM-REM transition and reveals the nonlinear, time-varying dampening effect of age on deep sleep, offering rigorous and interpretable biomarkers for complex physiological dynamics.
