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Giuseppe CAVALIERE (University of Bologna) “Bootstrap Inference in the Presence of Bias “
Time: 11.30 pm
Date: 31th of March 2022
Room 3001+ zoom
Giuseppe CAVALIERE (University of Bologna) “Bootstrap Inference in the Presence of Bias ”
Abstract : In this paper we consider bootstrap inference for estimators which are (asymptotically) biased. We show that, even in cases where the bias term cannot be consistently estimated, valid inference can successfully be restored by proper implementations of the bootstrap. We do this by focusing on the properties of the bootstrap p-values, and on the fact that, for some bootstrap schemes, the large-sample distribution of the bootstrap p-values, albeit not uniformly distributed, do not depend on the bias. When such schemes are found, we show that the prepivoting approach of Beran (1987, 1988), originally proposed to deliver higher-order refinements, restores bootstrap validity by properly transforming the original bootstrap p-values into asymptotically uniform random variables. We further propose different methods for feasible implementation of prepivoting. Specifically, we introduce a plug-in approach, based on estimation of the nuisance parameters appearing in the asymptotic distribution of the bootstrap p-values, and an automated method based on the double bootstrap. For both approaches, we provide very general high-level conditions that imply validity of bootstrap inference. Importantly, our assumptions cover estimators and statistics which are not asymptotically Gaussian. To illustrate the practical relevance of our results, and to show how to implement them in applied problems, we discuss five applications of the main ideas: (i) a simple location model for i.i.d. data, possibly with infinite variance; (ii) regression models with omitted controls; (iii) inference on a target parameter based on model averaging; (iv) ridge-type regularized estimators; and (v) dynamic panel data models.
Joint work : Silvia Goncalves [McGill U] and Morten Nielsen [U Aarhus]
Jean-Michel ZAKOIAN (CREST)