  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.
