Suppose we are testing a large number ($p$) hypothesis tests. Most commonly, a correction is applied to control the false discovery rate (FDR) at a low value, say $\alpha$. But now imagine a want to report the top 10 features with the largest test statistics, regardless of whether the corresponding p-values are significant or not. Is there a way to estimate the corresponding false discovery proportion (FDP)? Hence I fix the number of discoveries and want to estimate the FDP, rather than fixing the FDR and letting the number of discoveries vary as it is usually done.
I imagine just taking the 10th smallest Benjamini-Hochberg adjusted p-value or tail area false discovery rate will not be a valid estimator. Any pointers to existing literature or terminology would be appreciated.