A cross-validation based estimation of the proportion of true null hypotheses

Célisse, Alain; Robin, Stephane

Document type :

Compte-rendu et recension critique d'ouvrage

DOI :

10.1016/j.jspi.2010.04.014

Title :

A cross-validation based estimation of the proportion of true null hypotheses

Author(s) :

Célisse, Alain [Auteur correspondant]
Mathématiques et Informatique Appliquées [MIA-Paris]
Laboratoire Paul Painlevé - UMR 8524 [LPP]
Robin, Stephane [Auteur]
Mathématiques et Informatique Appliquées [MIA-Paris]

Journal title :

Journal of Statistical Planning and Inference

Pages :

3132-3147

Publisher :

Elsevier

Publication date :

2010

ISSN :

0378-3758

English keyword(s) :

multiple testing
false discovery rate
cross-validation
density estimation
histograms

HAL domain(s) :

Sciences du Vivant [q-bio]

English abstract : [en]

In the multiple testing context, a challenging problem is the estimation of the proportion pi(0) of true null hypotheses. A large number of estimators of this quantity rely on identifiability assumptions that either appear ...
Show more >In the multiple testing context, a challenging problem is the estimation of the proportion pi(0) 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 can be at least relaxed. The proposed estimator (pi) over cap (0) results from density estimation by histograms, and cross-validation. Several consistency results are derived under independence. A new (plug-in) multiple testing procedure (MTP) is also described, based on the Benjamini and Hochberg procedure (BH-procedure) and the proposed estimator. This procedure is asymptotically optimal, provides the asymptotic desired false discovery rate (FDR) control, and is more powerful than the BH-procedure. The non-asymptotic behavior of (pi) over cap is finally assessed through several simulation experiments. It outperforms numerous existing estimators in usual settings, and remains accurate with "U-shape" densities where other estimators usually fail. It does not exhibit any strong sensitivity to dependence. With m block-structured dependent data, it stays reliable up to a within block correlation rho = 0.5, when m/50 blocks are used.Show less >

Language :

Anglais

Popular science :

Non

Collections :

Laboratoire Paul Painlevé - UMR 8524

Source :

Harvested from HAL

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