Bootstrap Confidence Sets and Hypothesis Tests

Abstract

In this chapter, we study the applications of the bootstrap in two main components of statistical inference: constructing confidence sets and testing hypotheses. Five different bootstrap confidence sets are introduced in Section 4.1. Asymptotic properties and asymptotic comparisons of these five bootstrap confidence sets and the confidence sets obtained by normal approximation are given in Section 4.2. More sophisticated techniques for bootstrap confidence sets have been developed in recent years, some of which are described in Section 4.3. Fixed sample comparisons of various confidence sets are made in Section 4.4 through empirical simulation studies. Bootstrap hypothesis tests are introduced in Section 4.5.