EXCHANGEABLY WEIGHTED BOOTSTRAPS OF THE GENERAL EMPIRICAL PROCESS

We consider an exchangeably weighted bootstrap of the general function -indexed empirical process. We find sufficient conditions on the boots trap weights for the central limit theorem to hold for the bootstrappe d empirical process, almost surely and in probability. The results res emble those of Gine and Zinn for Efron's bootstrap. As a corollary we obtain a result on the almost sure convergence in distribution of the Efron-bootstrapped empirical process with arbitrary sample size. A lar ge number of bootstrap resampling schemes emerge as special cases of o ur results.