We propose a new variable selection procedure for a functional linear model with multiple scalar responses and multiple functional predictors. This method is based on basis expansions of the involved functional predictors and coefficients that lead to a multivariate linear regression model. Then a criterion by means of which the variable selection problem reduces to that of estimating a suitable set is introduced. Estimation of this set is achieved by using appropriate penalizations of estimates of this criterion, so leading to our proposal. A simulation study that permits to investigate the effectiveness of the proposed approach and to compare it with existing methods is given.

翻译：我们提出了一种针对包含多个标量响应变量与多个函数型预测变量的函数线性模型的新变量选择方法。该方法基于对参与建模的函数型预测变量及其系数进行基函数展开，从而构建一个多元线性回归模型。随后引入一个准则，将变量选择问题转化为对特定集合的估计问题。通过对该准则的估计量施加适当的惩罚项实现该集合的估计，由此形成本文的提议。我们进行了模拟研究，以考察所提方法的有效性，并将其与现有方法进行比较。