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Multiple testing of one-sided hypotheses: combining Bonferroni and the bootstrap

Author

Listed:
  • Joseph P. Romano
  • Michael Wolf

Abstract

In many multiple testing problems, the individual null hypotheses (i) concern univariate parameters and (ii) are one-sided. In such problems, power gains can be obtained for bootstrap multiple testing procedures in scenarios where some of the parameters are 'deep in the null' by making certain adjustments to the null distribution under which to resample. In this paper, we compare a Bonferroni adjustment that is based on finite-sample considerations with certain 'asymptotic' adjustments previously suggested in the literature.

Suggested Citation

  • Joseph P. Romano & Michael Wolf, 2017. "Multiple testing of one-sided hypotheses: combining Bonferroni and the bootstrap," ECON - Working Papers 254, Department of Economics - University of Zurich.
    • Handle: RePEc:zur:econwp:254
    as

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    File URL: https://www.zora.uzh.ch/id/eprint/138641/1/econwp254.pdf
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    References listed on IDEAS

    as
    1. Joseph P. Romano & Azeem M. Shaikh & Michael Wolf, 2014. "A Practical Two‐Step Method for Testing Moment Inequalities," Econometrica, Econometric Society, vol. 82, pages 1979-2002, September.
    2. Donald W. K. Andrews & Panle Jia Barwick, 2012. "Inference for Parameters Defined by Moment Inequalities: A Recommended Moment Selection Procedure," Econometrica, Econometric Society, vol. 80(6), pages 2805-2826, November.
    3. Joseph P. Romano & Michael Wolf, 2005. "Exact and Approximate Stepdown Methods for Multiple Hypothesis Testing," Journal of the American Statistical Association, American Statistical Association, vol. 100, pages 94-108, March.
    4. Halbert White, 2000. "A Reality Check for Data Snooping," Econometrica, Econometric Society, vol. 68(5), pages 1097-1126, September.
    5. Hansen, Peter Reinhard, 2005. "A Test for Superior Predictive Ability," Journal of Business & Economic Statistics, American Statistical Association, vol. 23, pages 365-380, October.
    6. Hsu, Po-Hsuan & Hsu, Yu-Chin & Kuan, Chung-Ming, 2010. "Testing the predictive ability of technical analysis using a new stepwise test without data snooping bias," Journal of Empirical Finance, Elsevier, vol. 17(3), pages 471-484, June.
    7. Donald W. K. Andrews & Gustavo Soares, 2010. "Inference for Parameters Defined by Moment Inequalities Using Generalized Moment Selection," Econometrica, Econometric Society, vol. 78(1), pages 119-157, January.
    Full references (including those not matched with items on IDEAS)

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    More about this item

    Keywords

    Bonferroni; multiple hypothesis testing; stepwise method;
    All these keywords.

    JEL classification:

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

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