|LAJOS HORVÁTH, Department of Mathematics, University of Utah, Salt Lake City, Utah 84112, USA|
|Best approximations for bootstrapped processes with applications|
We study the asymptotic properties of bootstrapped empirical processes based on ``naive'' and weighted bootstrap. We show that the order of the best possible approximation for the bootstrapped processes cannot be better than and we construct sequences of Brownian bridges where this rate is achieved. We discuss applications of the main results to density estimation and change-point detection.