Tests for a null hypothesis whose specification involves an unknown nuisance parameter may be obtained by inverting a bootstrap confidence region for the parameter being tested or by constructing a simulated null distribution for the test statistic. The power of either test against certain alternatives involving the same unknown nuisance parameter can itself be estimated by simulation.
"Simulated Power Functions." Ann. Statist. 14 (1) 151 - 173, March, 1986. https://doi.org/10.1214/aos/1176349847