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On the Number of Bootstrap Repetitions for Bootstrap Standard Errors, Confidence Intervals, and Tests

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Abstract

This paper considers the problem of choosing the number of bootstrap repetitions B for bootstrap standard errors, confidence intervals, and tests. For each of these problems, the paper provides a three-step method for choosing B to achieve a desired level of accuracy. Accuracy is measured by the percentage deviation of the bootstrap standard error estimate, confidence interval endpoint(s), test's critical value, or test's p-value based on B bootstrap simulations from the corresponding ideal bootstrap quantities for which B = infinity. Monte Carlo simulations show that the proposed methods work quite well. The results apply quite generally to parametric, semiparametric, and nonparametric models with independent and dependent data. The results apply to the standard nonparametric iid bootstrap, moving block bootstraps for time series data, parametric and semiparametric bootstraps, and bootstraps for regression models based on bootstrapping residuals.

Suggested Citation

  • Donald W.K. Andrews & Moshe Buchinsky, 1997. "On the Number of Bootstrap Repetitions for Bootstrap Standard Errors, Confidence Intervals, and Tests," Cowles Foundation Discussion Papers 1141R, Cowles Foundation for Research in Economics, Yale University.
    • Handle: RePEc:cwl:cwldpp:1141r
    Note: CFP 1069.
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    File URL: https://cowles.yale.edu/sites/default/files/files/pub/d11/d1141-r.pdf
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    1. Hall, Peter & Horowitz, Joel L, 1996. "Bootstrap Critical Values for Tests Based on Generalized-Method-of-Moments Estimators," Econometrica, Econometric Society, vol. 64(4), pages 891-916, July.
    2. Hall, Peter & Martin, Michael A., 1991. "On the error incurred using the bootstrap variance estimate when constructing confidence intervals for quantiles," Journal of Multivariate Analysis, Elsevier, vol. 38(1), pages 70-81, July.
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    1. > Econometrics > Econometric Theory > Bootstrap Methods

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    Cited by:

    1. Joon Y. Park, 2003. "Bootstrap Unit Root Tests," Econometrica, Econometric Society, vol. 71(6), pages 1845-1895, November.
    2. Jafry, Yusuf & Schuermann, Til, 2004. "Measurement, estimation and comparison of credit migration matrices," Journal of Banking & Finance, Elsevier, vol. 28(11), pages 2603-2639, November.
    3. Chwila Adam & Żądło Tomasz, 2020. "On the choice of the number of Monte Carlo iterations and bootstrap replicates in Empirical Best Prediction," Statistics in Transition New Series, Statistics Poland, vol. 21(2), pages 35-60, June.
    4. Paul EHLING & Sofia B. RAMOS, 2003. "Geographical versus Industrial Diversification: A Mean Variance Spanning Approach," FAME Research Paper Series rp80, International Center for Financial Asset Management and Engineering.
    5. Giannopoulos, Kostas & Tunaru, Radu, 2005. "Coherent risk measures under filtered historical simulation," Journal of Banking & Finance, Elsevier, vol. 29(4), pages 979-996, April.
    6. Adam Chwila & Tomasz Żądło, 2020. "On the choice of the number of Monte Carlo iterations and bootstrap replicates in Empirical Best Prediction," Statistics in Transition New Series, Polish Statistical Association, vol. 21(2), pages 35-60, June.
    7. de Peretti Christian & Siani Carole, 2004. "Neural Tests for Conditional Heteroskedasticity in ARCH-M Models," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, vol. 8(3), pages 1-24, September.
    8. Hanson, Samuel & Schuermann, Til, 2006. "Confidence intervals for probabilities of default," Journal of Banking & Finance, Elsevier, vol. 30(8), pages 2281-2301, August.
    9. Leonardo Gasparini & Walter Sosa, 2001. "Assessing Aggregate Welfare: Growth and Inequality in Argentina," Latin American Journal of Economics-formerly Cuadernos de Economía, Instituto de Economía. Pontificia Universidad Católica de Chile., vol. 38(113), pages 49-71.
    10. Carole Siani & Christian de Peretti, 2006. "Bootstrapping Neural tests for conditional heteroskedasticity," Computing in Economics and Finance 2006 301, Society for Computational Economics.

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    More about this item

    Keywords

    Bootstrap; bootstrap repetitions; coefficient of excess kurtosis; confidence interval; density estimation; hypothesis test; p-value; quantile; simulation; standard error estimate;
    All these keywords.

    JEL classification:

    • C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Hypothesis Testing: General
    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General
    • C15 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Statistical Simulation Methods: General

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