Abstract: For the problem of testing symmetry of the error distribution in a nonparametric regression model, we investigate the asymptotic properties of the difference between the two empirical distribution functions of estimated residuals and their counterparts with opposite signs. The weak convergence of the difference process to a Gaussian process is shown. The covariance structure of this process depends heavily on the density of the error distribution, and for this reason the performance of a symmetric wild bootstrap procedure is discussed in asymptotic theory, and by means of a simulation study. In contrast to available procedures, the new test is also applicable under heteroscedasticity.
Key words and phrases: Empirical process of residuals, testing for symmetry, nonparametric regression.