Simpler Bootstrap Estimation of the Asymptotic Variance of U-Statistic Based Estimators

The bootstrap is a popular and useful tool for estimating the asymptotic variance of complicated estimators. Ironically, the fact that the estimators are complicated can make the standard bootstrap computationally burdensome because it requires repeated re-calculation of the estimator. In this paper, we propose a method which is specific to extremum estimators based on U-statistics. The contribution here is that rather than repeated re-calculation of the U-statistic-based estimator, we can recalculate a related estimator based on single-sums. A simulation study suggests that the approach leads to a good approximation to the standard bootstrap, and that if this is the goal, then our approach is superior to numerical derivative methods