When Does Fast Bootstrap Work?

Abstract

In classic statistical inference, the bootstrap stands out as a simple, powerful, and data-driven technique. However, when coping with massive data sets, which are increasingly prevalent these days, the bootstrap can be computationally infeasible. To speed up the bootstrap for massive data sets, the “bag of little bootstraps” has been invented in 2014. Despite its considerable popularity, little is known about the bag of little bootstraps’s theoretical properties, including reliability. Indeed, our preliminary results have already raised questions on the applicability of the bag of little bootstraps under a simple but important setting.

This talk will first introduce the bag of little bootstraps procedure and then investigate its theoretical applicability. Specifically, for this applicability, this talk will present a counterexample for the claimed sufficient condition in the literature and will, as a remedy, provide a hopefully correct, generic sufficient condition. This work is joint with P. Bertail, D. Politis, and S. Volgushev.