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Bootstrap confidence intervals and hypothesis tests for extrema of parameters

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  • Peter Hall
  • Hugh Miller

Abstract

The bootstrap provides effective and accurate methodology for a wide variety of statistical problems which might not otherwise enjoy practicable solutions. However, there still exist important problems where standard bootstrap estimators are not consistent, and where alternative approaches, for example the m-out-of-n bootstrap and asymptotic methods, also face significant challenges. One of these is the problem of constructing confidence intervals or hypothesis tests for extrema of parameters, for example for the maximum of p parameters where each has to be estimated from data. In the present paper we suggest approaches to solving this problem. We use the bootstrap to construct an accurate estimator of the joint distribution of centred parameter estimators, and we base the procedure, either a confidence interval or a hypothesis test, on that distribution estimator. Our methodology is designed so that it errs on the side of conservatism, modulo the small inaccuracy of the bootstrap step. Copyright 2010, Oxford University Press.

Suggested Citation

  • Peter Hall & Hugh Miller, 2010. "Bootstrap confidence intervals and hypothesis tests for extrema of parameters," Biometrika, Biometrika Trust, vol. 97(4), pages 881-892.
    • Handle: RePEc:oup:biomet:v:97:y:2010:i:4:p:881-892
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    File URL: http://hdl.handle.net/10.1093/biomet/asq045
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    Cited by:

    1. Francesca Di Iorio & Stefano Fachin, 2011. "A sieve bootstrap range test for poolability in dependent cointegrated panels," DSS Empirical Economics and Econometrics Working Papers Series 2011/2, Centre for Empirical Economics and Econometrics, Department of Statistics, "Sapienza" University of Rome.
    2. Castagnetti, Carolina & Rossi, Eduardo & Trapani, Lorenzo, 2015. "Inference on factor structures in heterogeneous panels," Journal of Econometrics, Elsevier, vol. 184(1), pages 145-157.
    3. Di Iorio, Francesca & Fachin, Stefano, 2012. "A simple sieve bootstrap range test for poolability in dependent cointegrated panels," Economics Letters, Elsevier, vol. 116(2), pages 154-156.
    4. Bulat Gafarov, 2019. "Simple subvector inference on sharp identified set in affine models," Papers 1904.00111, arXiv.org, revised Dec 2023.

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