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Multiple Testing of One-Sided Hypotheses: Combining Bonferroni and the Bootstrap

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Predictive Econometrics and Big Data (TES 2018)

Part of the book series: Studies in Computational Intelligence ((SCI,volume 753))

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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.

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Notes

  1. 1.

    This means that \(\hat{\sigma }_{n,s}\) is an estimator of the standard deviation of \(\hat{\theta }_{n,s}\).

  2. 2.

    More precisely, the improvement is a stepdown method.

  3. 3.

    Such a program is carried out in the moment inequality problem by [RSW14].

  4. 4.

    More precisely, the improvement is a stepdown method.

References

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Author information

Authors and Affiliations

  1. Departments of Economics and Statistics, Stanford University, Stanford, USA

    Joseph P. Romano

  2. Department of Economics, University of Zurich, Zurich, Switzerland

    Michael Wolf

Authors
  1. Joseph P. Romano
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  2. Michael Wolf
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Corresponding author

Correspondence to Michael Wolf .

Editor information

Editors and Affiliations

  1. Computer Science Department, University of Texas at El Paso, El Paso, Texas, USA

    Vladik Kreinovich

  2. International College, Chiang Mai University, Chiang Mai, Thailand

    Songsak Sriboonchitta

  3. International College, Chiang Mai University, Chiang Mai, Thailand

    Nopasit Chakpitak

A Detailed Monte Carlo Results

A Detailed Monte Carlo Results

1.1 A.1 Results for \(n = 50\)

See Tables 1, 2, 3 and 4.

Table 1. All \(\theta _s = 0\): FWE.
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Table 2. Five of the \(\theta _s = 0.4\): FWE | Power.
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Table 3. Five of the \(\theta _s = 0.4\) and S/2 of the \(\theta _s = -0.4\): FWE | Power.
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Table 4. Five of the \(\theta _s = 0.4\) and S/2 of the \(\theta _s = -0.8\): FWE | Power.
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1.2 A.2 Results for \(n=100\)

See Tables 5, 6, 7 and 8.

Table 5. All \(\theta _s = 0\): FWE.
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Table 6. Ten of the \(\theta _s = 0.3\): FWE | Power.
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Table 7. Ten of the \(\theta _s = 0.3\) and S/2 of the \(\theta _s = -0.3\): FWE | Power.
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Table 8. Ten of the \(\theta _s = 0.3\) and S/2 of the \(\theta _s = -0.6\): FWE | Power.
Full size table

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Romano, J.P., Wolf, M. (2018). Multiple Testing of One-Sided Hypotheses: Combining Bonferroni and the Bootstrap. In: Kreinovich, V., Sriboonchitta, S., Chakpitak, N. (eds) Predictive Econometrics and Big Data. TES 2018. Studies in Computational Intelligence, vol 753. Springer, Cham. https://doi.org/10.1007/978-3-319-70942-0_4

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  • DOI: https://doi.org/10.1007/978-3-319-70942-0_4

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-70941-3

  • Online ISBN: 978-3-319-70942-0

  • eBook Packages: EngineeringEngineering (R0)

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