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Bootstrap variance estimators with truncation

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  • Shao, Jun

Abstract

The bootstrap estimator of the asymptotic covariance matrix of a function of sample means or sample quantiles is inconsistent in some situations. Using the idea of truncation, we propose a modified bootstrap estimator and show its consistency under weak conditions. A simulation study shows that in terms of finite-sample performance, the gain in using truncation is substantial. The computation of our modified bootstrap estimator is much easier and cheaper than that of the estimator based on the quantiles of the bootstrap distribution. We show by simulation that with the same number of bootstrap replicates (in bootstrap Monte Carlo approximation), the modified bootstrap estimator is more accurate than the estimator based on the interquartile range of the bootstrap distribution.

Suggested Citation

  • Shao, Jun, 1992. "Bootstrap variance estimators with truncation," Statistics & Probability Letters, Elsevier, vol. 15(2), pages 95-101, September.
    • Handle: RePEc:eee:stapro:v:15:y:1992:i:2:p:95-101
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    Citations

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    Cited by:

    1. Goncalves, Silvia & White, Halbert, 2004. "Maximum likelihood and the bootstrap for nonlinear dynamic models," Journal of Econometrics, Elsevier, vol. 119(1), pages 199-219, March.
    2. Daniel Ackerberg & Xiaohong Chen & Jinyong Hahn & Zhipeng Liao, 2014. "Asymptotic Efficiency of Semiparametric Two-step GMM," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 81(3), pages 919-943.
    3. Salibian-Barrera, Matias, 2006. "Bootstrapping MM-estimators for linear regression with fixed designs," Statistics & Probability Letters, Elsevier, vol. 76(12), pages 1287-1297, July.
    4. Jinyong Hahn & Zhipeng Liao, 2021. "Bootstrap Standard Error Estimates and Inference," Econometrica, Econometric Society, vol. 89(4), pages 1963-1977, July.

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