We consider the problem of variable selection in varying-coefficient functional linear models, where multiple predictors are functions and a response is a scalar and depends on an exogenous variable. The varying-coefficient functional linear model is estimated by the penalized maximum likelihood method with the sparsity-inducing penalty. Tuning parameters that controls the degree of the penalization are determined by a model selection criterion. The proposed method can reveal which combination of functional predictors relates to the response, and furthermore how each predictor relates to the response by investigating coefficient surfaces. Simulation studies are provided to investigate the effectiveness of the proposed method. We also apply it to the analysis of crop yield data to investigate which combination of environmental factors relates to the amount of a crop yield.

翻译：我们考虑在不同、具有不同效益的功能线性模型中选择变量的问题,在这种模型中,多个预测器是功能,反应是卡路里,取决于外源变量。不同效益的功能线性模型是通过惩罚性最大可能性的方法和宽度诱导惩罚来估计的。控制惩罚程度的参数由示范选择标准来确定。拟议方法可以揭示哪些功能预测器组合与反应有关,以及每个预测器如何通过调查系数表面与反应有关。提供了模拟研究,以调查拟议方法的有效性。我们还将它用于分析作物产量数据,以调查哪些环境因素组合与作物产量有关。