In modern biomedical and econometric studies, longitudinal processes are often characterized by complex time-varying associations and abrupt regime shifts that are shared across correlated outcomes. Standard functional data analysis (FDA) methods, which prioritize smoothness, often fail to capture these dynamic structural features, particularly in high-dimensional settings. This article introduces Adaptive Joint Learning (AJL), a hierarchical regularization framework designed to integrate functional variable selection with structural changepoint detection in multivariate time-varying coefficient models. Unlike standard simultaneous estimation approaches, we propose a theoretically grounded two-stage screening-and-refinement procedure. This framework first synergizes adaptive group-wise penalization with sure screening principles to robustly identify active predictors, followed by a refined fused regularization step that effectively borrows strength across multiple outcomes to detect local regime shifts. We provide a rigorous theoretical analysis of the estimator in the ultra-high-dimensional regime (p >> n). Crucially, we establish the sure screening consistency of the first stage, which serves as the foundation for proving that the refined estimator achieves the oracle property-performing as well as if the true active set and changepoint locations were known a priori. A key theoretical contribution is the explicit handling of approximation bias via undersmoothing conditions to ensure valid asymptotic inference. The proposed method is validated through comprehensive simulations and an application to Sleep-EDF data, revealing novel dynamic patterns in physiological states.

翻译：在现代生物医学与计量经济学研究中，纵向过程常呈现出复杂的时变关联性以及相关结局间共享的突变状态转换。标准的函数型数据分析方法强调平滑性，往往难以捕捉这些动态结构特征，尤其在高维场景下。本文提出了自适应联合学习框架，这是一种旨在多元时变系数模型中整合函数型变量选择与结构变点检测的分层正则化方法。不同于标准的同步估计方法，我们提出了一种理论依据充分的两阶段筛选-精炼流程。该框架首先将自适应组惩罚与确定筛选原则相结合，以稳健识别活跃预测变量；随后通过精炼的融合正则化步骤，有效借助多结局间的信息共享来检测局部状态转换。我们在超高维情形下对估计量进行了严格的理论分析。关键的是，我们证明了第一阶段具有确定筛选一致性，这为论证精炼估计量具备预言机性质——即如同真实活跃集与变点位置已知时一样有效——奠定了基础。一项重要的理论贡献是通过欠平滑条件显式处理近似偏差，以确保有效的渐近推断。所提方法通过综合模拟实验及在Sleep-EDF数据集上的应用得到验证，揭示了生理状态中新颖的动态模式。