Suppose one is testing multiple hypotheses and, for a given FDR, computes Benjamini-Hochberg adjusted p-values. Furthermore, consider the classifier defined by $f(p; t) = \{\text{True if } p \ge t; \text{else False}\}$ where $p$ is the p-value from the statistical test and the classes are "null hypothesis is rejected" and "not rejected".
My question is: at the adjusted p-value threshold corresponding to the FDR, would we expect the classifier's false positive rate to equal the FDR?
