Dependency and false discovery rate: Asymptotics

By Helmut Finner, Thorsten Dickhaus, Markus Roters. 2007

105 citations recorded by the source corpus.

Some effort has been undertaken over the last decade to provide conditions for the control of the false discovery rate by the linear step-up procedure (LSU) for testing n hypotheses when test statistics are dependent. In this paper we investigate the expected error rate (EER) and the false discovery rate (FDR) in some extreme parameter configurations when n tends to infinity for test statistics being exchangeable under null hypotheses. All results are derived in terms of p-values. In a general setup we present a series of results concerning the interrelation of Simes' rejection curve and the (limiting) empirical distribution function of the p-values. Main objects under investigation are largest (limiting) crossing points between these functions, which play a key role in deriving explicit formulas for EER and FDR. As specific examples we investigate equi-correlated normal and t-variables in more detail and compute the limiting EER and FDR theoretically and numerically. A surprising limit behavior occurs if these models tend to independence.

Subfields: Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/15c790cfa8afff058ce02b342ebe20ee7c045750

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Citations in the corpus

Journal of the American Statistical Association Estimating False Discovery Proportion under Arbitrary Covariance Dependence Estimating False Discovery Proportion under Arbitrary Covariance Dependence (unknown): “Finner, Dickhaus, and Roters (2007) in their Theorem 2.1 also showed a result similar to Theorem 1 for the equal correlation case.”
Controlling the familywise error rate with plug‐in estimator for the proportion of true null hypotheses (2009, methodology): “This model was studied extensively in Finner et al. (2007); see example 2.2 and section 4 in Finner et al. (2007), Among others, it follows from the derivations in Finner et al. (2007) that the empirical CDF F̂In,0 of the p-values under null hypotheses satisfies limn0→∞{F̂In,0.”
Adaptive FDR control under independence and dependence (2007, methodology): “1, with parameter λ = α , - [FDR09- 1 2 ] The procedure proposed in Finner et al. (2009) and described in Section 3.”
Exact calculations for false discovery proportion with application to least favorable configurations (2010, methodology): “…inﬁnity; Chi (2007) computed the asymptotic rejection number distribution of the LSU procedure by introducing the criticality phenomenon [6], while Finner et al. (2007) computed the limiting FDR of the LSU procedure for positively correlated p -values (following an equicorrelated multivariate…”
An adaptive step-down procedure with proven FDR control under independence (2009, background): “Finner, Dickhaus and Roters [ 7 ] were interested in the form of an asymptoti-”