  We address the issue of lack-of-fit testing for a parametric quantile
regression. We propose a simple test that involves one-dimensional kernel
smoothing, so that the rate at which it detects local alternatives is
independent of the number of covariates. The test has asymptotically gaussian
critical values, and wild bootstrap can be applied to obtain more accurate ones
in small samples. Our procedure appears to be competitive with existing ones in
simulations. We illustrate the usefulness of our test on birthweight data.
