BOOTSTRAP CONFIDENCE-INTERVALS

This article surveys bootstrap methods for producing good approximate confidence intervals. The goal is to improve by an order of magnitude upon the accuracy of the standard intervals <(theta)over cap> +/- z((a lpha))<(sigma)over cap>, in a way that allows routine application even to very complicated problems. Both theory and examples are used to sh ow how this is done. The first seven sections provide a heuristic over view of four bootstrap confidence interval procedures: BCa, bootstrap- t, ABC and calibration. Sections 8 and 9 describe the theory behind th ese methods, and their close connection with the Likelihood-based conf idence interval theory developed by Barndorff-Nielsen, Cox and Reid an d others.