Weak Convergence of Smoothed and Nonsmoothed Bootstrap Quantile Estimates

Abstract

Under fairly general assumptions on the underlying distribution function, the bootstrap process, pertaining to the sample q-quantile, converges weakly in DR to the standard Brownian motion. Furthermore, weak convergence of a smoothed bootstrap quantile estimate is proved which entails that in this particular case the smoothed bootstrap estimate outperforms the nonsmoothed one.