Bootstrap Sampling Distributions

The bootstrap was discovered by Efron (1979), who coined the name. In this chapter, the bootstrap is developed as a general method to approximate the sampling distribution of a statistic, a pivot, or a root (defined below), in order to construct confidence regions for a parameter of interest. The use of the bootstrap to approximate a null distribution in the construction of hypothesis tests is also considered. Much of the theoretical foundations of the bootstrap are laid out in Bickel and Freedman (1981), Singh (1981), and Beran (1984). The development begins by focusing on the independent, identically distributed (i.i.d.) case.