Testing for symmetric error distribution in nonparametric regression models

Abstract

For the problem of testing symmetry of the error distribution in a nonparametric re-gression model we propose as a test statistic 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 co-variance 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 the available procedures the new test is also applicable under heteroscedasticity. AMS Classification: 62G10, 60F17