In this article we propose a boosting algorithm for regression with functional explanatory variables and scalar responses. The algorithm uses decision trees constructed with multiple projections as the "base-learners", which we call "functional multi-index trees". We establish identifiability conditions for these trees and introduce two algorithms to compute them. We use numerical experiments to investigate the performance of our method and compare it with several linear and nonlinear regression estimators, including recently proposed nonparametric and semiparametric functional additive estimators. Simulation studies show that the proposed method is consistently among the top performers, whereas the performance of any competitor relative to others can vary substantially across different settings. In a real example, we apply our method to predict electricity demand using price curves and show that our estimator provides better predictions compared to its competitors, especially when one adjusts for seasonality.

翻译：在本文中，我们提出了一个回归 with functional explanatory variables and scalar responses 的 boosting 算法。该算法使用采用多重投影的决策树作为“基学习器”，我们称之为“functional multi-index trees”。我们确定了这些树的可识别性条件，并引入了两个算法来计算它们。我们使用数值实验来研究我们的方法的性能，并将其与几种线性和非线性回归估计器进行比较，其中包括最近提出的非参数和半参数函数型加法估计器。模拟研究表明，所提出的方法始终位于表现最好的算法之一，而任何竞争者的表现相对于其他竞争者可能在不同的设置中存在较大差异。在一个真实的例子中，我们应用我们的方法来预测电力需求，使用价格曲线，结果显示我们的估计比其他竞争者提供更好的预测能力，特别是当调整季节性因素时。