Samuel Maistre, Pascal Lavergne, and Valentin Patilea, “Powerful nonparametric checks for quantile regression”, TSE Working Paper, n. 14-501, June 2014.
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.
Samuel Maistre, Pascal Lavergne, and Valentin Patilea, “Powerful nonparametric checks for quantile regression”, Journal of Statistical Planning and Inference, vol. 180, January 2017, pp. 13–29.