Bootstrap Inference in the Presence of Bias

Giuseppe Cavaliere*, Sílvia Gonçalves, Morten Ørregaard Nielsen, Edoardo Zanelli

*Corresponding author for this work

Research output: Contribution to journal/Conference contribution in journal/Contribution to newspaperJournal articleResearchpeer-review

Abstract

We consider bootstrap inference for estimators which are (asymptotically) biased. We show that, even when the bias term cannot be consistently estimated, valid inference can be obtained by proper implementations of the bootstrap. Specifically, we show that the prepivoting approach of Beran, originally proposed to deliver higher-order refinements, restores bootstrap validity by transforming the original bootstrap p-value into an asymptotically uniform random variable. We propose two different implementations of prepivoting (plug-in and double bootstrap), and provide general high-level conditions that imply validity of bootstrap inference. To illustrate the practical relevance and implementation of our results, we discuss five examples: (i) inference on a target parameter based on model averaging; (ii) ridge-type regularized estimators; (iii) nonparametric regression; (iv) a location model for infinite variance data; and (v) dynamic panel data models. Supplementary materials for this article are available online.

Original languageEnglish
JournalJournal of the American Statistical Association
ISSN0162-1459
DOIs
Publication statusAccepted/In press - 2024

Keywords

  • Asymptotic bias
  • Bootstrap
  • Incidental parameter bias
  • Model averaging
  • Nonparametric regression
  • Prepivoting

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