We develop a new method for variable selection in a nonlinear additive function-on-scalar regression (FOSR) model. Existing methods for variable selection in FOSR have focused on the linear effects of scalar predictors, which can be a restrictive assumption in the presence of multiple continuously measured covariates. We propose a computationally efficient approach for variable selection in existing linear FOSR using functional principal component scores of the functional response and extend this framework to a nonlinear additive function-on-scalar model. The proposed method provides a unified and flexible framework for variable selection in FOSR, allowing nonlinear effects of the covariates. Numerical analysis using simulation study illustrates the advantages of the proposed method over existing variable selection methods in FOSR even when the underlying covariate effects are all linear. The proposed procedure is demonstrated on accelerometer data from the 2003–2004 cohorts of the National Health and Nutrition Examination Survey (NHANES) in understanding the association between diurnal patterns of physical activity and demographic, lifestyle, and health characteristics of the participants.

中文翻译：

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非线性标量函数回归中的变量选择

我们开发了一种在非线性可加函数标量回归 (FOSR) 模型中选择变量的新方法。FOSR 中现有的变量选择方法侧重于标量预测变量的线性效应，在存在多个连续测量的协变量的情况下，这可能是一个限制性假设。我们提出了一种使用函数响应的函数主成分分数在现有线性 FOSR 中进行变量选择的计算高效方法，并将该框架扩展到非线性可加函数标量模型。所提出的方法为 FOSR 中的变量选择提供了一个统一且灵活的框架，允许协变量的非线性效应。使用模拟研究的数值分析说明了所提出的方法优于 FOSR 中现有变量选择方法的优点，即使潜在的协变量效应都是线性的。拟议的程序在 2003-2004 年国家健康和营养检查调查 (NHANES) 队列的加速度计数据上得到证明，以了解参与者的昼夜体育活动模式与人口统计、生活方式和健康特征之间的关联。