Regression problems with multiple functional predictors have been studied previously. In this paper, we investigate functional quantile linear regression with multiple functional predictors within the framework of reproducing kernel Hilbert spaces. The estimation procedure is based on an ${\ell }_1$-mixed-norm penalty. The learning rate of the estimator in prediction loss is established and a lower bound on the learning rate is also presented that matches the upper bound up to a logarithmic term.

中文翻译：

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再现核希尔伯特空间中高维函数分位数回归的最优预测

先前已经研究了具有多个功能预测器的回归问题。在本文中，我们在再现核希尔伯特空间的框架内研究了具有多个函数预测器的函数分位数线性回归。估计过程基于${\ell }_1$-混合规范惩罚。建立了预测损失中估计器的学习率，并且还提供了学习率的下限，该下限与上限匹配到对数项。