We are interested in the efficiency of the nonparametric estimation of the conditional quantile when the response variable is a scalar given a functional covariate. To do this, we adopt a technique which is based on the use of the k-Nearest Neighbors procedure to build a kernel estimator of this model. Then, we establish the uniform convergence in number of neighbors of the constructed estimator. Moreover, we discuss the optimal choices of different parameters that are involved in the model as well as the impacts of the obtained results. Finally, we show the applicability and efficiency of our methodology to investigate the fuel quality by using a Near-infrared spectroscopy dataset.

当响应变量是给定函数协变量的标量时，我们对条件分位数的非参数估计的效率感兴趣。为此，我们采用了一种基于k-最近邻居过程的技术来构建此模型的核估计器。然后，我们建立构造的估计量的邻居数量的一致收敛。此外，我们讨论了模型中涉及的不同参数的最佳选择，以及所获得结果的影响。最后，我们展示了使用近红外光谱数据集研究燃料质量的方法论的适用性和效率。