In this paper, we develop a new and effective approach to nonparametric quantile regression that accommodates ultrahigh-dimensional data arising from spatio-temporal processes. This approach proves advantageous in staving off computational challenges that constitute known hindrances to existing nonparametric quantile regression methods when the number of predictors is much larger than the available sample size. We investigate conditions under which estimation is feasible and of good overall quality and obtain sharp approximations that we employ to devising statistical inference methodology. These include simultaneous confidence intervals and tests of hypotheses, whose asymptotics is borne by a non-trivial functional central limit theorem tailored to martingale differences. Additionally, we provide finite-sample results through various simulations which, accompanied by an illustrative application to real-worldesque data (on electricity demand), offer guarantees on the performance of the proposed methodology.

翻译：本文提出了一种新颖有效的非参数分位数回归方法，适用于处理时空过程产生的高维数据。该方法能有效规避计算挑战，这些挑战在预测变量数量远大于可用样本量时，对现有非参数分位数回归方法构成显著障碍。我们研究了估计可行的条件及其整体质量，并获得了精确的近似结果，用于构建统计推断方法。这些方法包括同步置信区间和假设检验，其渐近性质由针对鞅差序列定制的非平凡泛函中心极限定理所支撑。此外，我们通过多种模拟实验提供了有限样本结果，并结合实际数据（电力需求）的示例应用，为所提方法的性能提供了保证。