The straightforward application of bootstrap methods to hypothesis testing is to estimate the confidence interval of the test statistic $\hat{\theta}$ by repeatedly calculating it on the bootstrapped samples (Let the statistic $\hat{\theta}$ sampled from bootstrap be called $\hat{\theta^*}$). We reject $H_0$ if the hypothesized parameter $\theta_0$ (which usually equals 0) lies outside of the confidence interval of $\hat{\theta^*}$.
I've read, that this method lacks some power. In the article by Hall P. and Wilson S.R. "Two Guidelines for Bootstrap Hypothesis Testing" (1992) it is written as the first guideline, that one should resample $\hat{\theta^*} - \hat{\theta}$, not the $\hat{\theta^*} - \theta_0$. And this is the part I don't understand.
Isn't that the $\hat{\theta^*} - \hat{\theta}$ measures just the bias of the estimator $\hat{\theta^*}$? For unbiased estimators the confidence intervals of this expression should always be smaller than $\hat{\theta^*} - \theta_0$, but I fail to see, what it has to do with testing for $\hat{\theta}=\theta_0$? There is nowhere I can see we put information about the $\theta_0$.
For those of you, who do not have access to this article, this is a quote of the relevant paragraph which comes immediately after the thesis:
To appreciate why this is important, observe that the test will involve rejecting $H_0$ if in $\left| \hat{\theta} - \theta_0\right|$ is "too large." If $\theta_0$ is a long way from true value of $\theta$ (i.e., if $H_0$ is grossly the error) then the difference $\left|\hat{\theta} - \theta_0 \right|$ will never look very much too big compared to the nonparametric bootstrap distribution of $\left| \hat{\theta} - \theta_0\right|$. A more meaningful comparison is with the distribution of $\left| \hat{\theta^*} - \hat{\theta}\right|$. In fact, if the true value of $\theta$ is $\theta_1$ then the power of the bootstrap test increases to 1 as $\left|\theta_1 - \theta_0\right|$ increases, provided test is based on resampling $\left| \hat{\theta^*} - \hat{\theta}\right|$ , but the power decreases to at most the significance level (as $\left|\theta_1 - \theta_0\right|$ increases) if the test is based on resampling $\left|\hat{\theta} - \theta_0\right|$