Improved null proportion estimators for multiple discrete tests with plug-in FDR control
Abstract
It is well known that the performance of the Benjamini-Hochberg (BH) procedure can be improved by incorporating estimators of the number or proportion of null hypotheses to yield an adaptive BH procedure which still controls FDR. Several such plug-in estimators have been proposed. For some of these, such as Storey’s estimator, plug-in FDR control has been established, while for some others, such as the Pounds–Cheng estimator, some gaps remain to be closed. These developments have largely focused on the case of continuous test statistics, where null p -values follow the uniform distribution. In the discrete setting, although these estimators continue to provide plug-in FDR control, they become overly conservative, leading to inefficient procedures. In this paper, a general class of estimators that encompasses the classical Storey and Pounds–Cheng estimators is introduced. Alongside, several generic strategies to mitigate conservativeness in the discrete setting are proposed by incorporating information about the null distribution functions. These strategies provably yield less conservative estimates while maintaining valid FDR control, and the resulting performance gains are illustrated on both real and simulated data. As a byproduct of a more general result, plug-in FDR control for the Pounds–Cheng estimator in the continuous case is also established.
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BibTeX
@article{meah2026improved,
title = {{Improved null proportion estimators for multiple discrete tests with plug-in FDR control}},
author = {Iqraa Meah and Sebastian Döhler},
journal = {Computational Statistics and Data Analysis},
year = {2026},
month = sep,
doi = {10.1016/j.csda.2026.108429},
url = {https://hal.science/hal-05734542v1},
note = {CC BY},
}
RIS
TY - JOUR
TI - Improved null proportion estimators for multiple discrete tests with plug-in FDR control
AU - Iqraa Meah
AU - Sebastian Döhler
PY - 2026
DA - 2026/09/01
JO - Computational Statistics and Data Analysis
DO - 10.1016/j.csda.2026.108429
UR - https://hal.science/hal-05734542v1
AB - It is well known that the performance of the Benjamini-Hochberg (BH) procedure can be improved by incorporating estimators of the number or proportion of null hypotheses to yield an adaptive BH procedure which still controls FDR. Several such plug-in estimators have been proposed. For some of these, such as Storey’s estimator, plug-in FDR control has been established, while for some others, such as the Pounds–Cheng estimator, some gaps remain to be closed. These developments have largely focused on the case of continuous test statistics, where null p -values follow the uniform distribution. In the discrete setting, although these estimators continue to provide plug-in FDR control, they become overly conservative, leading to inefficient procedures. In this paper, a general class of estimators that encompasses the classical Storey and Pounds–Cheng estimators is introduced. Alongside, several generic strategies to mitigate conservativeness in the discrete setting are proposed by incorporating information about the null distribution functions. These strategies provably yield less conservative estimates while maintaining valid FDR control, and the resulting performance gains are illustrated on both real and simulated data. As a byproduct of a more general result, plug-in FDR control for the Pounds–Cheng estimator in the continuous case is also established.
SN - 0167-9473
ER -