Bootstrap

Abstract

In Section 10.3 we obtained a central limit theorem for data-based estimators (Formula Presented) of cluster functionals (Formula Presented). Theorem 10.3.1 allows us to construct confidence intervals for (Formula Presented) of the form (Formula Presented) is the limiting variance of the estimator and (Formula Presented) quantile of the standard normal random variable. Unfortunately, in most cases, the limiting variance depends on unknown parameters and has a complicated form, often an infinite series, as can be seen in the examples of Section 10.4.