I came across this page and was surprised and confused by the following:
A naive person attempting to do a bootstrap test just calculates a P-value as something like
mean(tstat.star > tstat.hat)
where tstat.hat is the value of the test statistic calculated for the actual data and tstat.star is a vector of values of the test statistic calculated for bootstrap samples.
The resulting test is a valid hypothesis test in the sense that a test with nominal significance level α actually has that significance level.
But (a big but!) this test typically has no power. It rejects the null hypothesis with probability α regardless of what the alternative is. No matter how large the deviation of the true parameter value from the null hypothesis, the naive bootstrap test typically doesn't find any "statistical significance."
He goes on to say
There are a variety of special situations in which something that makes sense as a nonparametric bootstrap hypothesis test can be done. Efron and Tibshirani, Chapter 16 describe a few. But if you don't see a general principle in their explanation, don't worry. There isn't any.
I'm having a hard time coming up with an example in which the test has no power, regardless of the true parameter value. Also, based on the second quote, I suppose the standard examples for nonparametric hypothesis testing are considered by Geyer to be special situations?
I understand that for tests that don't involve just shuffling or otherwise manipulating data labels, it can be difficult to sample from the null hypothesis, but it seems that Geyer is already assuming a valid test, i.e., this is not the failure mode he has in mind.