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：传感器设备近年来在工程和健康研究中得到日益广泛的应用，所捕获的多维活动与生命体征信号可结合健康结局开展研究，为公共卫生提供依据。常用的方法是标量-函数回归模型，其中健康结局为标量响应，高维传感器信号为函数型协变量，但如何有效解释结果变得困难。本研究提出一种基于稀疏组套索函数正则化的新型功能型自适应双稀疏（FadDoS）估计量，该估计量通过函数型变量选择实现全局稀疏性，并通过系数函数内零子区间识别实现局部稀疏性。我们证明，在温和条件下，FadDoS估计量以有界速率收敛并满足Oracle性质。大量模拟研究验证了理论性质，并表明其相比现有方法具有优异性能。将方法应用于一项基于Kinect传感器的研究，该研究采用先进运动感应设备追踪老年人多个关节活动，并在社区老年人中开展，结果展示了FadDoS估计量如何有效刻画关节活动与身体健康评估之间的精细关联。所提方法不仅在Kinect传感器分析中有效，还可推广至同步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。