A BOOTSTRAP ADAPTIVE TEST FOR 2-WAY ANALYSIS OF VARIANCE

We propose a method to construct adaptive tests based on a bootstrap technique. The procedure leads to a nearly exact adaptive test depending on the size of the sample. With the use of the estimated Pitman's relative efficacy as selector statistic, we show that the adaptive test has a power that is asymptotically equal to the power of it's better component. We apply the idea to construct an adaptive test for two-way analysis of variance model. Finally, we use simulations to observe the behaviour of the method for small sample sizes.