Abstract Quantile functional linear regression was previously studied using functional principal component analysis. Here we consider the alternative penalized estimator based on the reproducing kernel Hilbert spaces (RKHS) setting. The motivation is that, for the functional linear (mean) regression, it has already been shown in Cai and Yuan (2012) that the approach based on RKHS performs better when the coefficient function does not align well with the eigenfunctions of the covariance kernel. We establish its optimal convergence rate in prediction risk using the Rademacher complexity to bound appropriate empirical processes. Some Monte Carlo studies are carried out for illustration.

中文翻译：

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再现核希尔伯特空间中分位数泛函线性回归的最优预测

摘要 分位数泛函线性回归以前曾使用泛函主成分分析进行过研究。在这里，我们考虑基于再生核希尔伯特空间 (RKHS) 设置的替代惩罚估计器。动机是，对于函数线性（均值）回归，Cai 和 Yuan（2012）已经表明，当系数函数与协方差核的特征函数不一致时，基于 RKHS 的方法性能更好。我们使用 Rademacher 复杂性来确定其在预测风险中的最佳收敛率，以限制适当的经验过程。进行了一些蒙特卡罗研究以进行说明。