Objectives and Overview
This chapter describes and illustrates computationally intensive nonparametric bootstrap methods to compute statistical intervals, primarily for continuous distributions. These methods require obtaining a sequence of simulated bootstrap samples, based on the given data. Then these bootstrap samples are used to generate corresponding bootstrap estimates.
As mentioned in the introduction to Chapter 5, nonparametric implies that no particular parametric distribution needs to be specified when applying the statistical method. The distribution-free methods introduced in Chapter 5 were also nonparametric. The nonparametric methods presented in this chapter, however, are not distribution-free because the statistical properties (e.g., coverage probabilities) of the procedures depend on the unspecified underlying probability distribution.
Although nonparametric bootstrap procedures do not require specification of a particular parametric distribution for the underlying data, they generally do not work well with small samples (e.g., fewer than ten observations for some applications) in the sense that the procedures have coverage probabilities that might be far from the specified nominal confidence level.
The alternative parametric bootstrap methods presented in Chapter 14 require one to specify the form of a parametric distribution for the given data. Such methods can lead to excellent approximate, or sometimes ...