The Convergence Rates Of The Weighted Bootstrap Distributions For Von Mises And U-statistics

摘要

It has been proved that the weighted bootstrap method for von Mises and U-statistics provides a feasible approximation to their sample distributions. In the paper, based on a variation of the Berry-Esseen theorem for U-statistics, we further develop such first-order convergence rate under weak conditions. Moreover, in view of maximum entropy, we provide a principle to choose the weights.