(1) Department of Mathematics, Indiana University, 47405 Bloomington, Indiana;(2) Department of Mathematical Sciences, University of Delaware, 501 Ewing Hall, 19716 Newark, Delaware
Abstract:
We obtain weighted approximations by a Brownian bridge to permutation and exchangeable processes and to appropriately defined inverse processes. Our results provide as special cases useful weighted approximations to the uniform empirical and quantile processes and to generalized bootstrapped versions of these processes. A number of other applications are discussed. Our approach is based on the Skorokhod embedding for martingales.