ON BOOTSTRAP HYPOTHESIS TESTING

We describe methods for constructing bootstrap hypothesis tests, illustrating our approach using analysis of variance. The importance of pivotalness is discussed. Pivotal statistics usually result in improved accuracy of level. We note that hypothesis tests and confidence intervals call for different methods of resampling, so as to ensure that accurate critical point estimates are obtained in the former case even when data fail to comply with the null hypothesis. Our main points are illustrated by a simulation study and application to three real data sets.