Currently, working with partially observed functional data has attracted a greatly increasing attention, since there are many applications in which each functional curve may be observed only on a subset of a common domain, and the incompleteness makes most existing methods for functional data analysis ineffective. In this paper, motivated by the appealing characteristics of conditional quantile regression, the authors consider the functional linear quantile regression, assuming the explanatory functions are observed partially on dense but discrete point grids of some random subintervals of the domain. A functional principal component analysis (FPCA) based estimator is proposed for the slope function, and the convergence rate of the estimator is investigated. In addition, the finite sample performance of the proposed estimator is evaluated through simulation studies and a real data application.

当前，使用部分观察到的功能数据引起了极大的关注，因为在许多应用中，每个功能曲线只能在一个公共域的子集上观察到，并且不完整使得大多数现有的功能数据分析方法无效。在本文中，受条件分位数回归的吸引人的特征的影响，作者考虑了函数线性分位数回归，假设在部分随机子区间的密集但离散的点网格上部分观察到了解释函数。针对斜率函数，提出了一种基于函数主成分分析的估计器，并研究了该估计器的收敛速度。此外，