This paper is written for a Festschrift in honour of Professor Marc Hallin and it proposes some developments on quantile regression. We connect our investigation to Marc's scientific production and we present some theoretical and methodological advances for quantiles estimation in non standard settings. We split our contributions in two parts. The first part is about conditional quantiles estimation for nonstationary time series: our approach combines local stationarity for Markov processes with quantile regression. The second part is about conditional quantiles estimation for the analysis of multivariate independent data in the presence of possibly large dimensional covariates: our procedure combines optimal transport theory with quantile regression forests. Monte Carlo studies illustrate numerically the performance of our methods and compare them to extant methods. The codes needed to replicate our results are available on our $\mathtt{GitHub}$ pages.

翻译：本文为致敬Marc Hallin教授而撰写的纪念文集而作，提出分位数回归领域的一些新进展。我们将研究内容与Marc的学术成果相联系，并针对非标准设定下的分位数估计提出若干理论和方法论创新。本文贡献分为两部分：第一部分研究非平稳时间序列的条件分位数估计，将马尔可夫过程的局部平稳性与分位数回归相结合；第二部分研究高维协变量背景下多元独立数据的条件分位数估计，将最优运输理论与分位数回归森林相结合。蒙特卡洛模拟从数值角度验证了所提方法的性能，并与现有方法进行了对比。用于复现结果的代码已上传至我们的$\mathtt{GitHub}$页面。