Bootstrap Methods: The Classical Theory and Recent Development

Abstract

Bootstrap is a resampling method for statistical inference . Under fairly general conditions, the technique can be used to approximate sampling distributions of almost any statistics, by recycling data from the observed sample, that is, resampling. In this article, we review the theoretical tenets of bootstrapping, focusing primarily on the fundamental property of consistency , while showing examples where lack of consistency can lead to failures of the method. We also describe residual and pairs bootstrap methods in linear models, as well as their applications in low‐ and high‐dimensional problems. Finally, we discuss a modified bootstrap procedure in big data situations.