Lihua Lei sharpens worst-case FDR bounds in common-factor Gaussian models

Lihua Lei shared a thread of results on false discovery rate (FDR) under dependence, focusing on a common-factor Gaussian model. According to his posts, the key point is that the worst-case FDR inflation can be pinned down at the right order in this setting, which sharpens understanding of BH under correlated Gaussian testing and shows earlier logarithmic upper bounds were not the end of the story.

Key result

Lei says he proved a lower bound stating that for small nominal level `q`, the worst-case FDR is at least `(1/(2√π)-o(1)) q√log(1/q)`. A direct implication is that as `q → 0`, the ratio `FDR/q` diverges, so there cannot be a universal constant `C` that guarantees `FDR ≤ Cq` for all models in this class. He also noted that the `q√log(1/q)` form was somewhat surprising to him.

Relation to prior work

Lei compared this with @weijie444's FDR linking theorem, which—without relying on Gaussian assumptions—gives an upper bound of order `q log(1/q)`. In the common-factor Gaussian setting, Lei says the logarithmic factor can be improved, and that he also proved an upper bound matching the lower bound in order.

Context

He further said the result was inspired by a counterexample from @EdgarDobriban. In his framing, the message is that Gaussian structure allows a sharper characterization of worst-case FDR inflation than more general dependence-agnostic results.

2026-07-17 ~ 2026-07-17 · 5 related posts