Maintaining the exchangeability assumption for a two-group permutation test in the non-randomized setting

Abstract

In this note, we develop a new two-group bootstrap-permutation test that utilizes the tail-extrapolated quantile function estimator for the bootstrap component. This test is an extension of the standard two-group permutation test, that through its construction is defined to meet the exchangeability assumption, and thus it guarantees that the type I error is appropriately bounded by definition. This methodology is particularly useful in the non-randomized two-group setting for which the exchangeability assumption for the traditional two-group permutation test is untestable. We develop some theoretical results for the new test, followed by a simulation study and an example.

Keywords:

• bootstrap
• nonparametric
• quantile function

Acknowledgements

We very much appreciate the referee's comments, which led to a substantially improved presentation.