This work proposes new inference methods for the estimation of a regression coefficient of interest in quantile regression models. We consider high-dimensional models where the number of regressors potentially exceeds the sample size but a subset of them suffice to construct a reasonable...

We consider several variants of a likelihood-ratio process for quantile regression designed to test composite hypotheses about the combined influence of several covariates over an entire range of conditional quantile functions. A closely related process is proposed as a goodness-of-fit criterion...