Asymptotic degeneracy of the Benjamini–Hochberg estimator for non-null hypothesis proportions

Estimating the proportion of true null hypotheses ( π 0 ) is essential for improving the performance of multiple testing procedures. In this paper, we investigate the asymptotic behavior of the Benjamini–Hochberg (BH) estimator, showing that it converges to 1 under the assumption of exchangeable p-values. This asymptotic degeneracy implies that, for a large number of tests, the adaptive BH procedure offers no significant advantage over the original BH algorithm. Simulations indicate that this asymptotic degeneracy may also hold under other dependence structures, such as autoregressive structures. Through simulations, we also demonstrate that Storey’s estimator exhibits similar overestimation and conservative behavior under certain dependence structures, highlighting the need for improvements to the estimator proposed by Schweder and Spjøtvoll (1982) .