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A note on methods of restoring consistency to the bootstrap

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  • Richard Samworth

Abstract

We consider the property of consistency and its relevance for determining the performance of the bootstrap. We analyse various parametric bootstrap approximations to the distributions of the Hodges and Stein estimators, whose behaviour is typical of that of super-efficient estimators employed in wavelet regression, kernel density estimation and nonparametric curve fitting. Our results reveal not only some of the difficulties in selecting good modifications to the intuitive bootstrap, but also that inconsistent bootstrap approximations may perform better than consistent versions even in large samples. Copyright Biometrika Trust 2003, Oxford University Press.

Suggested Citation

  • Richard Samworth, 2003. "A note on methods of restoring consistency to the bootstrap," Biometrika, Biometrika Trust, vol. 90(4), pages 985-990, December.
    • Handle: RePEc:oup:biomet:v:90:y:2003:i:4:p:985-990
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    Cited by:

    1. Donald W.K. Andrews & Sukjin Han, 2008. "Invalidity of the Bootstrap and the m Out of n Bootstrap for Interval Endpoints Defined by Moment Inequalities," Cowles Foundation Discussion Papers 1671, Cowles Foundation for Research in Economics, Yale University.
    2. Kascha, Christian & Trenkler, Carsten, 2011. "Bootstrapping the likelihood ratio cointegration test in error correction models with unknown lag order," Computational Statistics & Data Analysis, Elsevier, vol. 55(2), pages 1008-1017, February.
    3. Andrews, Donald W.K. & Guggenberger, Patrik, 2009. "Incorrect asymptotic size of subsampling procedures based on post-consistent model selection estimators," Journal of Econometrics, Elsevier, vol. 152(1), pages 19-27, September.
    4. Giurcanu, Mihai C., 2012. "Bootstrapping in non-regular smooth function models," Journal of Multivariate Analysis, Elsevier, vol. 111(C), pages 78-93.
    5. Ian W. McKeague & Min Qian, 2015. "An Adaptive Resampling Test for Detecting the Presence of Significant Predictors," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 110(512), pages 1422-1433, December.
    6. Zhexiao Lin & Fang Han, 2023. "On the failure of the bootstrap for Chatterjee's rank correlation," Papers 2303.14088, arXiv.org, revised Apr 2023.
    7. Richard A. Lockhart & Richard J. Samworth, 2017. "Comments on: High-dimensional simultaneous inference with the bootstrap," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 26(4), pages 734-739, December.

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