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

Author

Listed:
  • Bo E. Honore
  • Luojia Hu

Abstract

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.

Suggested Citation

  • Bo E. Honore & Luojia Hu, 2015. "Simpler Bootstrap Estimation of the Asymptotic Variance of U-statistic Based Estimators," Working Paper Series WP-2015-7, Federal Reserve Bank of Chicago.
  • Handle: RePEc:fip:fedhwp:wp-2015-07
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    References listed on IDEAS

    as
    1. Alan Sule & Honoré Bo E. & Hu Luojia & Leth-Petersen Søren, 2014. "Estimation of Panel Data Regression Models with Two-Sided Censoring or Truncation," Journal of Econometric Methods, De Gruyter, vol. 3(1), pages 1-20, January.
    2. Bhattacharya, Debopam, 2008. "A Permutation-Based Estimator For Monotone Index Models," Econometric Theory, Cambridge University Press, vol. 24(3), pages 795-807, June.
    3. Horowitz, Joel L, 1992. "A Smoothed Maximum Score Estimator for the Binary Response Model," Econometrica, Econometric Society, vol. 60(3), pages 505-531, May.
    4. Manski, Charles F., 1975. "Maximum score estimation of the stochastic utility model of choice," Journal of Econometrics, Elsevier, vol. 3(3), pages 205-228, August.
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    More about this item

    Keywords

    U-statistics; bootstrap; inference; numerical derivatives;
    All these keywords.

    JEL classification:

    • C10 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - General
    • C18 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Methodolical Issues: General

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