Simpler Bootstrap Estimation of the Asymptotic Variance of U-Statistic Based Estimators
21 Pages Posted: 7 Sep 2017 Last revised: 8 Sep 2017
Date Written: September, 2015
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 Honor and Hu (2015), we propose a computationally simpler bootstrap procedure based on repeated re-calculation of one-dimensional estimators. The applicability of that approach is quite general. In this paper, we propose an alternative method which is specific to extremum estimators based on U-statistics. The contribution here is that rather than repeated re-calculating 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.
Keywords: U-statistics, bootstrap, inference, numerical derivatives
JEL Classification: C10, C18
Suggested Citation: Suggested Citation