Statistical Intervals, 2nd Edition

Chapter 14 Parametric Bootstrap and Other Simulation-Based Statistical Intervals

Objectives and Overview

This chapter describes and illustrates computationally intensive parametric bootstrap and other simulation-based methods to compute statistical intervals, primarily for continuous distributions. These methods, like the nonparametric bootstrap methods in Chapter 13, require obtaining a sequence of simulated bootstrap samples based on the given data that are then used to generate corresponding bootstrap estimates. The parametric bootstrap procedures presented in this chapter (like all of the other chapters in this book other than Chapters 5 and 13) require one to specify a parametric distribution for the given data. These methods can lead to excellent approximate, or sometimes exact, procedures for computing statistical intervals, even for small samples, when the chosen distribution is correct. Parametric bootstrap methods may, however, result in misleading answers if the chosen distribution is seriously in error.

The topics discussed in this chapter are:

• The basic concept of using simulation and parametric bootstrap methods to obtain confidence intervals (Section 14.1).
• Methods for generating parametric bootstrap samples and obtaining bootstrap estimates (Section 14.2).
• How to obtain parametric confidence intervals by using the simulated distribution of a pivotal quantity (Section 14.3).
• How to obtain parametric confidence intervals by using the simulated distribution of ...