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Bootstrap confidence sets under model misspecification

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  • Vladimir Spokoiny
  • Mayya Zhilova

Abstract

A multiplier bootstrap procedure for construction of likelihood-based con dence sets is considered for nite samples and a possible model misspeci cation. Theoretical results justify the bootstrap consistency for a small or moderate sample size and allow to control the impact of the parameter dimension p: the bootstrap approximation works if p3=n is small. The main result about bootstrap consistency continues to apply even if the underlying parametric model is misspeci ed under the so called Small Modeling Bias condition. In the case when the true model deviates signi cantly from the considered parametric family, the bootstrap procedure is still applicable but it becomes a bit conservative: the size of the constructed con dence sets is increased by the modeling bias. We illustrate the results with numerical examples for misspeci ed constant and logistic regressions.

Suggested Citation

  • Vladimir Spokoiny & Mayya Zhilova, 2014. "Bootstrap confidence sets under model misspecification," SFB 649 Discussion Papers SFB649DP2014-067, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
    • Handle: RePEc:hum:wpaper:sfb649dp2014-067
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    References listed on IDEAS

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    5. Victor Chernozhukov & Denis Chetverikov & Kengo Kato, 2012. "Gaussian approximations and multiplier bootstrap for maxima of sums of high-dimensional random vectors," Papers 1212.6906, arXiv.org, revised Jan 2018.
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    Cited by:

    1. Mayya Zhilova, 2015. "Simultaneous likelihood-based bootstrap confidence sets for a large number of models," SFB 649 Discussion Papers SFB649DP2015-031, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
    2. Demian Pouzo, 2014. "Bootstrap Consistency for Quadratic Forms of Sample Averages with Increasing Dimension," Papers 1411.2701, arXiv.org, revised Aug 2015.

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    More about this item

    Keywords

    likelihood-based bootstrap con dence set; misspeci ed model; nite sample size; multiplier bootstrap; weighted bootstrap; Gaussian approximation; Pinsker's inequality;
    All these keywords.

    JEL classification:

    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
    • C15 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Statistical Simulation Methods: General

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