We propose a novel method for variable selection in functional linear concurrent regression. Our research is motivated by a fisheries footprint study where the goal is to identify important time‐varying sociostructural drivers influencing patterns of seafood consumption, and hence the fisheries footprint, over time, as well as estimating their dynamic effects. We develop a variable‐selection method in functional linear concurrent regression extending the classically used scalar‐on‐scalar variable‐selection methods like the lasso, smoothly clipped absolute deviation (SCAD) and minimax concave penalty (MCP). We show that in functional linear concurrent regression the variable‐selection problem can be addressed as a group lasso, and their natural extension: the group SCAD or a group MCP problem. Through simulations, we illustrate that our method, particularly with the group SCAD or group MCP, can pick out the relevant variables with high accuracy and has minuscule false positive and false negative rate even when data are observed sparsely, are contaminated with noise and the error process is highly non‐stationary. We also demonstrate two real data applications of our method in studies of dietary calcium absorption and fisheries footprint in the selection of influential time‐varying covariates.

中文翻译：

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函数线性并发回归中的变量选择

我们提出了一种新的函数线性并发回归中变量选择的方法。我们的研究受到渔业足迹研究的启发，该研究的目的是确定重要的随时间变化的社会结构驱动因素，这些因素会随着时间的推移影响海产品的消费方式，进而影响渔业足迹，并估算其动态影响。我们在函数线性并发回归中开发了一种变量选择方法，扩展了经典使用的标量对标量变量选择方法，如套索，平滑限幅绝对偏差（SCAD）和最小极大凹罚（MCP）。我们表明，在函数线性并发回归中，变量选择问题可以作为组套索及其自然扩展来解决：组SCAD或组MCP问题。通过仿真，我们说明了我们的方法，尤其是对于SCAD小组或MCP小组，即使在稀疏地观察数据，被噪声污染且错误处理过程非常不稳定的情况下，也可以高精度地选择相关变量，并且假阳性率和假阴性率也很小。我们还展示了我们的方法在选择影响性时变协变量的饮食中钙吸收和渔业足迹研究中的两个实际数据应用。