On the false discovery proportion convergence under Gaussian equi-correlation

Sylvain Delattre (1) , Etienne Roquain (1)

1 LPMA - Laboratoire de Probabilités et Modèles Aléatoires

We study the convergence of the false discovery proportion (FDP) of the Benjamini-Hochberg procedure in the Gaussian equi-correlated model, when the correlation $\rho_m$ converges to zero as the hypothesis number $m$ grows to infinity. By contrast with the standard convergence rate $m^{1/2}$ holding under independence, this study shows that the FDP converges to the false discovery rate (FDR) at rate $\{\min(m,1/\rho_m)\}^{1/2}$ in this equi-correlated model.

Keywords: False discovery rate; Donsker theorem; equi-correlation; functional Delta method; $p$-value

Domains: Statistics [math.ST]; Statistics Theory [stat.TH]

Sylvain Delattre, Etienne Roquain. On the false discovery proportion convergence under Gaussian equi-correlation. 2010. ⟨hal-00497134v1⟩