Bootstrap Inference in the Presence of Bias

• 成果类型: Article
• 署名作者: Cavaliere, Giuseppe; Goncalves, Silvia; Nielsen, Morten Orregaard; Zanelli, Edoardo
• 署名单位: University of Bologna; McGill University; Aarhus University
• 刊物名称: JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION
• ISSN/ISSBN: 0162-1459
• DOI: 10.1080/01621459.2023.2284980
• 发表日期: 2024
• 页码: 2908-2918
• 关键词: CONFIDENCE BANDS; error; asymptotics; regression

摘要

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.