Multiple bootstrap tests and their application

Abstract

We review bootstrap methods for testing statistical hypotheses. We begin with single hypothesis testing and give an example of its use. We then consider multiple testing based on Holm's step-down procedure and discuss how the bootstrap can incorporate relevant correlation and distributional characteristics. These techniques are applied to tests for zeros of transfer functions of linear systems at different frequencies, conventionally solved using "large sample" approximations. Our results highlight the applicability of the bootstrap in a situation where asymptotic results are not valid.<>