Powerful nonparametric checks for quantile regression

- We develop a new omnibus lack-of-fit test for a parametric quantile regression.
- It involves one-dimensional kernel smoothing only whatever the covariates dimension.
- The test is easy to apply and compare favorably to competitors in simulations.

We propose a new and simple lack-of-fit test for a parametric quantile regression. It 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 and in an empirical application with several covariates.