Sensor devices have been increasingly used in engineering and health studies recently, and the captured multi-dimensional activity and vital sign signals can be studied in association with health outcomes to inform public health. The common approach is the scalar-on-function regression model, in which health outcomes are the scalar responses while high-dimensional sensor signals are the functional covariates, but how to effectively interpret results becomes difficult. In this study, we propose a new Functional Adaptive Double-Sparsity (FadDoS) estimator based on functional regularization of sparse group lasso with multiple functional predictors, which can achieve global sparsity via functional variable selection and local sparsity via zero-subinterval identification within coefficient functions. We prove that the FadDoS estimator converges at a bounded rate and satisfies the oracle property under mild conditions. Extensive simulation studies confirm the theoretical properties and exhibit excellent performances compared to existing approaches. Application to a Kinect sensor study that utilized an advanced motion sensing device tracking human multiple joint movements and conducted among community-dwelling elderly demonstrates how the FadDoS estimator can effectively characterize the detailed association between joint movements and physical health assessments. The proposed method is not only effective in Kinect sensor analysis but also applicable to broader fields, where multi-dimensional sensor signals are collected simultaneously, to expand the use of sensor devices in health studies and facilitate sensor data analysis.

翻译：近年来，传感器设备在工程与健康研究中日益普及，所捕获的多维活动与生命体征信号可与健康结局相关联，为公共卫生提供信息。常用方法是标量-函数回归模型，其中健康结局作为标量响应，而高维传感器信号作为函数协变量，但如何有效解释结果变得困难。本研究基于多函数预测变量的稀疏群组套索函数正则化，提出一种新的功能自适应双稀疏估计器，该估计器可通过函数变量选择实现全局稀疏性，并通过系数函数内的零子区间识别实现局部稀疏性。我们证明FadDoS估计器在温和条件下以有界速率收敛并满足预言性。大量模拟研究证实了理论性质，并展现出优于现有方法的卓越性能。在一项采用先进运动传感设备追踪人体多关节运动、针对社区居住老年人开展的Kinect传感器研究中，应用结果表明FadDoS估计器能有效刻画关节运动与身体健康评估间的精细关联。所提方法不仅对Kinect传感器分析有效，还可推广至同时采集多维传感器信号的更广泛领域，从而拓展传感器设备在健康研究中的应用并促进传感器数据分析。