Bootstrap Condence Intervals

This article surveys bootstrap methods for producing good approximate condence intervals. The goal is to improve by an order of magnitude upon the accuracy of the standard intervals O z e e O , in a way that allows routine application even to very complicated problems. Both theory and examples are used to show how this is done. The rst seven sections provide a heuristic overview of four bootstrap condence interval procedures: BCa, bootstrap-t, ABC and calibration. Sections 8 and 9 describe the theory behind these methods, and their close connec- tion with the likelihood-based condence interval theory developed by Barndorff-Nielsen, Cox and Reid and others. Condence intervals have become familiar friends in the applied statistician's collection of data-analytic tools. They combine point estima- tion and hypothesis testing into a single inferen- tial statement of great intuitive appeal. Recent advances in statistical methodology allow the con- struction of highly accurate approximate condence intervals, even for very complicated probability models and elaborate data structures. This article discusses bootstrap methods for constructing such intervals in a routine, automatic way. Two distinct approaches have guided condence interval construction since the 1930's. A small cata- logue of exact intervals has been built up for special situations, like the ratio of normal means or a sin- gle binomial parameter. However, most condence intervals are approximate, with by far the favorite approximation being the standard interval