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Quantifying the failure of bootstrap likelihood ratio tests

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  • Mathias Drton
  • Benjamin Williams

Abstract

When testing geometrically irregular parametric hypotheses, the bootstrap is an intuitively appealing method to circumvent difficult distribution theory. It has been shown, however, that the usual bootstrap is inconsistent in estimating the asymptotic distributions involved in such problems. This paper is concerned with the asymptotic size of likelihood ratio tests when critical values are computed using the inconsistent bootstrap. We clarify how the asymptotic size of such a test can be obtained from the size of the corresponding bootstrap test in the relevant limiting normal experiment. For boundary problems, that is, hypotheses given by convex cones, we show the bootstrap test to always be anticonservative, and we compute the size numerically for different two-dimensional examples. The examples illustrate that the size can be below or above the nominal level, and reveal that the relationship between the size of the test and the geometry of the considered hypotheses is surprisingly subtle. Copyright 2011, Oxford University Press.

Suggested Citation

  • Mathias Drton & Benjamin Williams, 2011. "Quantifying the failure of bootstrap likelihood ratio tests," Biometrika, Biometrika Trust, vol. 98(4), pages 919-934.
    • Handle: RePEc:oup:biomet:v:98:y:2011:i:4:p:919-934
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    File URL: http://hdl.handle.net/10.1093/biomet/asr033
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    Cited by:

    1. Ghosal, Rahul & Ghosh, Sujit K., 2022. "Bayesian inference for generalized linear model with linear inequality constraints," Computational Statistics & Data Analysis, Elsevier, vol. 166(C).
    2. Chunlin Wang & Paul Marriott & Pengfei Li, 2022. "A note on the coverage behaviour of bootstrap percentile confidence intervals for constrained parameters," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 85(7), pages 809-831, October.
    3. Zhexiao Lin & Fang Han, 2023. "On the failure of the bootstrap for Chatterjee's rank correlation," Papers 2303.14088, arXiv.org, revised Apr 2023.

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