Bootstrap Methods

Abstract

In this chapter, we describe various commonly used bootstrap methods that have been proposed in the literature. Section 2.2 begins with a brief description of Efron’s (1979) bootstrap method based on simple random sampling of the data, which forms the basis for almost all other bootstrap methods. In Section 2.3, we describe the famous example of Singh (1981), which points out the limitation of this resampling scheme for dependent variables. In Section 2.4, we present bootstrap methods for time-series models driven by iid variables, such as the autoregression model. In Sections 2.5, 2.6, and 2.7, we describe various block bootstrap methods. A description of the subsampling method is given in Section 2.8. Bootstrap methods based on the discrete Fourier transform of the data are described in Section 2.9, while those based on the method of sieves are presented in Section 2.10.