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Bootstrap inference in the presence of bias

Author

Listed:
  • Giuseppe Cavaliere
  • S'ilvia Gonc{c}alves
  • Morten {O}rregaard Nielsen
  • Edoardo Zanelli

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 (1987, 1988), 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.

Suggested Citation

  • Giuseppe Cavaliere & S'ilvia Gonc{c}alves & Morten {O}rregaard Nielsen & Edoardo Zanelli, 2022. "Bootstrap inference in the presence of bias," Papers 2208.02028, arXiv.org, revised Nov 2023.
    • Handle: RePEc:arx:papers:2208.02028
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    References listed on IDEAS

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