On the performance of FDR control: Constraints and a partial solution

By Zhiyi Chi. 2007

51 citations recorded by the source corpus.

The False Discovery Rate (FDR) paradigm aims to attain certain control on Type I errors with relatively high power for multiple hypothesis testing. The Benjamini–Hochberg (BH) procedure is a wellknown FDR controlling procedure. Under a random effects model, we show that, in general, unlike the FDR, the positive FDR (pFDR) of the BH procedure cannot be controlled at an arbitrarily low level due to the limited evidence provided by the observations to separate false and true nulls. This results in a criticality phenomenon, which is characterized by a transition of the procedure’s power from being positive to asymptotically 0 without any reduction in the pFDR, once the target FDR control level is below a positive critical value. To address the constraints on the power and pFDR control imposed by the criticality phenomenon, we propose a procedure which applies BH-type procedures at multiple locations in the domain of p-values. Both analysis and simulations show that the proposed procedure can attain substantially improved power and pFDR control.

Subfields: Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/6470ca07d9fe23f4f364a6584da954417644fb94

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Citations in the corpus

The Bayes oracle and asymptotic optimality of multiple testing procedures under sparsity (2010, methodology): “2) β = 0, that is, the criticality phenomenon of [10] does not occur.”
Exact calculations for false discovery proportion with application to least favorable configurations (2010, methodology): “This corroborates previous asymptotic studies in the so-called “subcritical” case (see [6, 7]).”
Simultaneous control of all false discovery proportions in large-scale multiple hypothesis testing (2016, methodology): “Note the contrast with comparable results, e.g. for BH, where for fixed α it can easily be shown under the model (13) (Chi, 2007) that, if γ < 1, plim (m,n)→∞ |Bα,m,n| m = 1− γ 1− αγ , implying that, if γ > 0, Bα,m,n is always asymptotically ‘too large’ for fixed α.”
Semi-Supervised Novelty Detection (2010, methodology): “Chi (2007) develops a procedure based on growing rejection intervals around a finite number of fixed control points in[0,1] .”