When your signals are correlated, BH needs a haircut

Question

Standard Benjamini-Hochberg (BH) guarantees FDR control under independence or positive dependence. But financial signals are often correlated in messy, unknown ways.

How does the Benjamini-Yekutieli (BY) procedure fix FDR control under arbitrary dependence, and how much power does it cost on a concrete example?

Accepted Answer

The fix. BY uses the same sort-and-compare recipe as BH, but shrinks each threshold by c(m) = \sum{i=1}^{m} 	frac1i (the mth harmonic number). Reject the largest rank k with p{(k)} \le \frac{k}{m\,c(m)}\,\alpha. This modification guarantees FDR \le \alpha for any dependence structure among the tests, at the price of a uniformly stricter bar. The cost, worked. Take m = 10, \alpha = 0.05, and the sorted p-values 0.001,\ 0.008,\ 0.012,\ 0.021,\ 0.030,\ 0.040,\ 0.060,\ 0.200,\ 0.300,\ 0.500. Here c(10) = 1 + 	frac12 + \dots + 	frac{1}{10} \approx 2.929. The BY thresholds are 	frac{k}{10 	ime…

When your signals are correlated, BH needs a haircut

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