# Exchangeably Weighted Bootstraps of Martingale Difference Arrays under the Uniformly Integrable Entropy

Published in Journal of Stochastic Analysis, 2020

### S. Alvarez-Andrade and S. Bouzebda

In the present paper, we are mainly interested in Cramér-type results for the weighted bootstrap of the $U$-statistics. The method of proof is based on the Hoeffding decomposition according to the bootstrapped Cramér transform together with the contraction technique. Finally, we investigate theU-statistics indexed by a one dimensional symmetric random walk.