The problem of estimating the spatio-functional quantile regression for a given spatial mixing structure $(X_{\mathbf{i}},Y_{\mathbf{i}})\in \mathcal{F}\times \mathbb{R}$, when $\mathbf{i}\in {\mathbb{Z}}^N$, $N\ge 1$ and $\mathcal{F}$ is a separable Hilbert space, is investigated. We construct and compare four estimators of the regression quantile. The proposed estimators cover the two main aspects of the statistical analysis, namely the parametric and nonparametric approaches. Precisely, using a parametric approach, we construct two estimators that are based respectively on the B-spline smoothing and the PCA regression. The other two estimators are constructed by using a non-parametric approach, namely the local constants method and the local linear method. Then, we establish the asymptotic properties of the four constructed estimators, and we examine their feasibility for finite size samples (i) on simulated data, and (ii) on real climatological data, which confirm the usefulness of our methodologies in practice.

给定空间混合结构的时空分位数回归估计问题 $（X_{\mathbf{一世}}，{ÿ}_{\mathbf{一世}}）\in \mathcal{F}\times \mathbb{[R}$， 什么时候 $\mathbf{一世}\in {\mathbb{ž}}^{ñ}$， $ñ\ge \mathrm{1个}$ 和 $\mathcal{F}$是一个可分离的希尔伯特空间，正在研究中。我们构造并比较了回归分位数的四个估计量。提议的估计量涵盖统计分析的两个主要方面，即参数方法和非参数方法。精确地，使用参数方法，我们构造了两个分别基于B样条平滑和PCA回归的估计量。其他两个估计量是通过使用非参数方法构造的，即局部常数方法和局部线性方法。然后，我们建立了四个构造的估计量的渐近性质，并检验了它们在有限大小样本上的可行性（i）模拟数据和（ii）真实气候数据，这证实了我们方法论在实践中的有用性。