Scope of Resampling Methods for Dependent Data

Abstract

The bootstrap is a computer-intensive method that provides answers to a large class of statistical inference problems without stringent structural assumptions on the underlying random process generating the data. Since its introduction by Efron (1979), the bootstrap has found its application to a number of statistical problems, including many standard ones, where it has outperformed the existing methodology as well as to many complex problems where conventional approaches failed to provide satisfactory answers. However, it is not a panacea for every problem of statistical inference, nor does it apply equally effectively to every type of random process in its simplest form. In this monograph, we shall consider certain classes of dependent processes and point out situations where different types of bootstrap methods can be applied effectively, and also look at situations where these methods run into problems and point out possible remedies, if there is one known.