Mora, J., and A. Pérez-Alonso
Journal of Nonparametric Statistics – 21.4 (2009): 441-452.

Keywords: specification testing, nonparametric regression, empirical processes

Abstract: We discuss how to test whether the distribution of regression errors belongs to a parametric family of continuous distribution functions, making no parametric assumption about the conditional mean or the conditional variance in the regression model. We propose using test statistics that are based on a martingale transform of the estimated empirical process. We prove that these statistics are asymptotically distribution-free, and two Monte Carlo experiments show that they work reasonably well in practice.