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：本文提出一种适用于函数型解释变量与标量响应变量的回归提升算法。该算法以通过多投影构建的决策树作为"基学习器"，我们称之为"函数多指标树"。我们建立了这些树的可识别条件，并提出了两种计算算法。通过数值实验考察方法的性能，并将其与多种线性和非线性回归估计量进行比较，包括近期提出的非参数与半参数函数型加性估计量。仿真研究表明，所提方法始终表现优异，而其他竞争方法在不同设定下的相对性能差异显著。在真实案例中，我们应用该方法利用价格曲线预测电力需求，结果表明，特别是考虑季节性调整后，我们的估计量相比其他方法能提供更优的预测。