On the false discovery proportion convergence under Gaussian equi-correlation

TL;DR

This paper investigates how the false discovery proportion (FDP) behaves under Gaussian equi-correlation as the number of hypotheses increases, revealing a convergence rate dependent on the correlation decay.

Contribution

It provides a novel analysis of FDP convergence rates in Gaussian equi-correlated models, extending understanding beyond independent hypotheses.

Findings

FDP converges to FDR at rate  \, \,  \, \, ext{min}(m,1/ ho_m)^{1/2}

Convergence rate differs from the standard ^{1/2} under independence

Results highlight the impact of correlation decay on FDP behavior.

Abstract

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.