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Prepivoting by weighted bootstrap iteration

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  • Stephen M. S. Lee

Abstract

Prepivoting by conventional bootstrap iteration is known to yield a progressively more accurate pivot in certain problems, and has important application in the construction of confidence limits and estimation of null distributions. We investigate the theoretical effects of weighted bootstrap iteration on prepivoting and show that each weighted bootstrap iteration, with weights chosen carefully but empirically, is asymptotically equivalent to two consecutive conventional bootstrap iterations. In terms of reducing the order of error, prepivoting can therefore be carried out much more efficiently if based on weighted bootstrap iterations. This is shown for a variety of problem settings, including the smooth function model, M-estimation and the regression context. A numerical illustration is provided, demonstrating the potential practical usefulness of weighted prepivoting. Copyright Biometrika Trust 2003, Oxford University Press.

Suggested Citation

  • Stephen M. S. Lee, 2003. "Prepivoting by weighted bootstrap iteration," Biometrika, Biometrika Trust, vol. 90(2), pages 393-410, June.
    • Handle: RePEc:oup:biomet:v:90:y:2003:i:2:p:393-410
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    Cited by:

    1. Lu, H.Y. Kevin & Young, G. Alastair, 2012. "Parametric bootstrap under model mis-specification," Computational Statistics & Data Analysis, Elsevier, vol. 56(8), pages 2410-2420.
    2. Davidson, Russell, 2017. "A discrete model for bootstrap iteration," Journal of Econometrics, Elsevier, vol. 201(2), pages 228-236.
    3. Lee, Stephen M.S. & Young, G. Alastair, 2005. "Parametric bootstrapping with nuisance parameters," Statistics & Probability Letters, Elsevier, vol. 71(2), pages 143-153, February.
    4. G. Alastair Young, 2003. "Better bootstrapping by constrained prepivoting," Metron - International Journal of Statistics, Dipartimento di Statistica, Probabilità e Statistiche Applicate - University of Rome, vol. 0(2), pages 227-242.
    5. Peter Hall & D. M. Titterington & Jing‐Hao Xue, 2009. "Tilting methods for assessing the influence of components in a classifier," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 71(4), pages 783-803, September.

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