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. The second part is about conditional quantiles estimation for the analysis of multivariate independent data in the presence of possibly large dimensional covariates. Monte Carlo studies illustrate numerically the performance of our methods and compare them to some extant techniques.

翻译：本文为纪念Marc Hallin教授而作，旨在探讨分位数回归的若干进展。我们将研究内容与Marc的学术成果相联系，针对非标准场景下的分位数估计提出一些理论与方法上的创新。本文贡献分为两部分：第一部分讨论非平稳时间序列的条件分位数估计；第二部分研究存在可能高维协变量时，多元独立数据的条件分位数估计。蒙特卡洛模拟实验展示了所提方法的数值表现，并与现有技术进行了对比。