On "Strong Control, Conservative Point Estimation and Simultaneous Conservative Consistency of False Discovery Rates" : Does a Large Number of Tests Obviate Confidence Intervals of the Fdr?

A previously proved theorem gives sufficient conditions for an estimator of the false discovery rate (FDR) to conservatively converge to the FDR with probability 1 as the number of hypothesis tests increases, even for small sample sizes. It does not follow that several thousand tests ensure that the estimator has moderate variance under those conditions. In fact, they can hold even if the test statistics have long-range correlations, which yield unacceptably wide confidence intervals, as observed in genomic data when there are 8 or 16 individuals (microarrays) per group. Thus, informative FDR estimation will include some measure of its reliability