## The Annals of Statistics

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

Zhiyi Chi

#### Abstract

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 well-known 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.

#### Article information

Source
Ann. Statist., Volume 35, Number 4 (2007), 1409-1431.

Dates
First available in Project Euclid: 29 August 2007

https://projecteuclid.org/euclid.aos/1188405616

Digital Object Identifier
doi:10.1214/009053607000000037

Mathematical Reviews number (MathSciNet)
MR2351091

Zentralblatt MATH identifier
1125.62075

#### Citation

Chi, Zhiyi. On the performance of FDR control: Constraints and a partial solution. Ann. Statist. 35 (2007), no. 4, 1409--1431. doi:10.1214/009053607000000037. https://projecteuclid.org/euclid.aos/1188405616

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