Three methods to apply the bootstrap correctly to hypothesis testing

Abstract

In this paper we discuss three methods to apply the bootstrap correctly to hypothesis testing. For each of these methods a simple example is considered, namely testing the variance of a population. The shortcoming associated with implementing bootstrap testing procedures incorrectly is analysed by making use of this example. Some theoretical properties of the corresponding bootstrap critical values are derived. The results of a simulation study are presented to provide empirical comparison between the different methods and to substantiate the theoretical findings