On the best approximation for bootstrapped empirical processes (Q1272996)

The authors consider the approximation of bootstrapped empirical processes by Brownian bridges and obtain a lower bound for the approximation error. This result implies that the best-possible rate of approximation is \(n^{-1/2}\log n\), which corresponds to the well-known Komlós-Major-Tusnády result on the approximation of empirical processes.