2008/04/08 by Alain Célisse, Alain Celisse, Stéphane Robin +2 · 4 citations
Decision Sciences · Mathematics · #Applied mathematics #Computer science #Context (archaeology) #Data mining #Estimator #False discovery rate #Identifiability #Independence (probability theory) #Mathematics #Mean squared error #Multiple comparisons problem #Null (SQL) #Null hypothesis #Optimal Experimental Design Methods #Statistical Methods and Bayesian Inference #Statistical Methods in Clinical Trials #Statistics #math.ST #stat.TH
paper · pdf · doi:10.48550/arxiv.0804.1189
published in arXiv (Cornell University) (Cornell University) · 21 pages
arxiv created 2008/04/08 · openalex publication_date 2008/04/08 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
In the multiple testing context, a challenging problem is the estimation of the proportion π0 of true-null hypotheses. A large number of estimators of this quantity rely on identifiability assumptions that either appear to be violated on real data, or may be at least relaxed. Under independence, we propose an estimator π0 based on density estimation using both histograms and cross-validation. Due to the strong connection between the false discovery rate (FDR) and π0, many multiple testing procedures (MTP) designed to control the FDR may be improved by introducing an estimator of π0. We provide an example of such an improvement (plug-in MTP) based on the procedure of Benjamini and Hochberg. Asymptotic optimality results may be derived for both π0 and the resulting plug-in procedure. The latter ensures the desired asymptotic control of the FDR, while it is more powerful than the BH-procedure. Finally, we compare our estimator of π0 with other widespread estimators in a wide range of simulations. We obtain better results than other tested methods in terms of mean square error (MSE) of the proposed estimator. Finally, both asymptotic optimality results and the interest in tightly estimating π0 are confirmed (empirically) by results obtained with the plug-in MTP.