We investigate functional additive quantile regression that models the conditional quantile of a scalar response by nonparametric effects of a functional predictor. We model the nonparametric effects of the principal component scores as additive components which are approximated by B-splines. We also select the relevant components using a nonconvex SCAD penalty. We establish that, when the relevant components are known, the convergence rate of the estimator using the estimated principal component scores is the same as that using the true scores. We also show that the estimator based on relevant components is a local solution of the SCAD penalized quantile regression problem. The practical performance of the proposed method is illustrated via simulation studies and an empirical application to the corn yield data.

中文翻译：

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函数可加分位数回归

我们研究了功能加性分位数回归，它通过功能预测器的非参数效应对标量响应的条件分位数进行建模。我们将主成分分数的非参数效应建模为由 B 样条近似的加性成分。我们还使用非凸 SCAD 惩罚来选择相关组件。我们确定，当相关成分已知时，使用估计的主成分分数的估计器的收敛速度与使用真实分数的收敛速度相同。我们还表明，基于相关组件的估计器是 SCAD 惩罚分位数回归问题的局部解决方案。通过模拟研究和对玉米产量数据的实证应用说明了所提出方法的实际性能。