Strong approximations for weighted bootstrap of empirical and quantile processes with applications

The main purpose of this paper is to investigate the strong approximation of the weighed bootstrap of empirical and quantile processes. The bootstrap idea is to reweight the original empirical distribution by stochastic weights. Our results are applied in two concrete statistical problems: the QQ–QQ processes as well as the kernel-type density estimator. Finally, a general notion of bootstrapped empirical quantile processes, from randomly censored data, constructed by exchangeably weighting samples is presented.