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On Efficient Estimators of the Proportion of True Null Hypotheses in a Multiple Testing Setup

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  • Van Hanh Nguyen
  • Catherine Matias

Abstract

type="main" xml:id="sjos12091-abs-0001"> We consider the problem of estimating the proportion θ 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 [0,1] with prior probability θ and a non-parametric density f . We discuss asymptotic efficiency results and establish that two different cases occur whether f 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.

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  • Van Hanh Nguyen & Catherine Matias, 2014. "On Efficient Estimators of the Proportion of True Null Hypotheses in a Multiple Testing Setup," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 41(4), pages 1167-1194, December.
  • Handle: RePEc:bla:scjsta:v:41:y:2014:i:4:p:1167-1194
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    File URL: http://hdl.handle.net/10.1111/sjos.12091
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    References listed on IDEAS

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    2. Rohit Kumar Patra & Bodhisattva Sen, 2016. "Estimation of a two-component mixture model with applications to multiple testing," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 78(4), pages 869-893, September.

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