Abstract:
This paper discusses how to choose the number of bootstrap samples when performing bootstrap tests. There are two important issues that arise when the number of bootstraps is finite. One is bias in the estimation of bootstrap $P$ values or critical values, and the second is loss of power. We discuss an easy way to avoid bias and thus obtain exact tests if the underlying test statistic is pivotal. We also propose a simple pretest procedure for choosing the number of bootstrap samples so as to avoid power loss, and we illustrate its performance using sampling experiments.