On Efficient Estimators of the Proportion of True Null Hypotheses in a Multiple Testing Setup. (8th April 2014)

• Record Type: Journal Article
• Authors: Nguyen, Van Hanh; Matias, Catherine
• Is Part Of: Scandinavian journal of statistics. Volume 41:Number 4(2014:Dec.)
• Page Start: 1167
• Page End: 1194
• Publication Date: 2014-04-08
• Subjects: Statistics -- Periodicals; 310
• DOI: 10.1111/sjos.12091
• Languages: English
• ISSNs: 0303-6898

Abstract

<abstract abstract-type="main" id="sjos12091-abs-0001"> <title>ABSTRACT</title> <p id="sjos12091-para-0001">We consider the problem of estimating the proportion <bold><italic>θ</italic></bold> of true null hypotheses in a multiple testing context. The setup is classically modelled through a semiparametric mixture with two components: a uniform distribution on interval <bold><italic>[0, 1]</italic></bold> with prior probability <bold><italic>θ</italic></bold> and a non‐parametric density <bold><italic>f</italic></bold>. We discuss asymptotic efficiency results and establish that two different cases occur whether <bold><italic>f</italic></bold> vanishes on a non‐empty interval or not. In the first case, we exhibit estimators converging at a parametric rate, compute the optimal asymptotic variance and conjecture that no estimator is asymptotically efficient (i.e. attains the optimal asymptotic variance). In the second case, we prove that the quadratic risk of any estimator does not converge at a parametric rate. We illustrate those results on simulated data.</p> </abstract>