Implementing the wild bootstrap using a two point distribution

We consider the problem of selecting the auxiliary distribution to implement the wild bootstrap for regressions featuring heteroscedasticity of unknown form. Asymptotic refinements are nominally obtained by choosing a distribution with second and third moments equal to 1. We show that this stipulation may fail in practice, due to the distortion imposed on higher moments. We propose a new class of two-point distributions and suggest using the Kolmogorov-Smirnov statistic as a selection criterion. The results are illustrated by a Monte Carlo experiment.