Bootstrapping rank statistics

The bootstrap, which provides powerful approximations for many classes of statistics, is studied for simple linear rank statistics employing bounded and smooth score functions. To verify consistency we view a rank statistic as a statistic induced by a statistical functional psi which is evaluated at a pair of dependent signed measures. Thus, we can apply the von Mises method to verify asymptotic results for the bootstrap. The strong consistency of the bootstrap distribution estimator is derived for the bootstrap based on resampling from the original data. Further, the residual bootstrap is studied. The accuracy of the bootstrap approximations for small sample sizes is studied by simulations. The simulations indicate that the bootstrap provides better results than a normal approximation.