Proof: No Universal Constant Bound for FDR Under Correlated Factors
lihua_lei_stat · x · 2026-07-17
In a statistics/ML theory study, the author proved a mathematical lower bound for the False Discovery Rate (FDR).
For a smaller nominal level q, the worst-case FDR is at least (1/(2√π)−o(1)) q√log(1/q). This means that as q approaches 0, the ratio FDR/q is unbounded. Consequently, a universal constant bound that uniformly constrains all nominal levels, number of hypotheses, means, and correlation matrices cannot exist. The author also proved a matching-order upper bound for a Gaussian model inspired by correlated factors.
Related event: Lihua Lei sharpens worst-case FDR bounds in common-factor Gaussian models(5 posts)→
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