Giuseppe Cavaliere, Sílvia Gonçalves, Morten Ørregaard Nielsen, Edoardo Zanelli
arXiv 3 Aug 2022 · Econometrics · publishedJournal of the American Statistical Association (2023) · 9 citations (OpenAlex)
arXiv:2208.02028 · PDF · DOI · OpenAlex · Extracted main text
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.
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