We introduce a goodness of fit process for quantile regression analogous to the conventional R2 statistic of least squares regression. Several related inference processes designed to test composite hypothese about the combined effect of several covariates over an entire range of conditional...

Quantile regression has emerged as an essential statistical tool of contemporary empirical economics and biostatistics. Complementing classical least squares regression methods which are designed to estimate conditional mean models, quantile regression provides an ensemble of techniques for...

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...