Simpler bootstrap estimation of the asymptotic variance of u-statistic based estimators*


  • This research was supported by the National Science Foundation and the Gregory C. Chow Econometric Research Program at Princeton University and presented at the Federal Reserve Bank of Chicago. The opinions expressed here are those of the authors and not necessarily those of the Federal Reserve Bank of Chicago or the Federal Reserve System. We are thankful to Reka Zempleni for excellent research assistance and to Michael Jansson and Anders P. Nielsen for constructive comments. The most recent version of this paper can be found at

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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.

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