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Multiple testing and post hoc bounds for heterogeneous data

Abstract : This manuscript presents my contributions in three areas of multiple testing where data heterogeneity can be exploited to better detect false null hypotheses or improve signal detection while controlling false positives: p-value weighting, discrete tests, and post hoc inference. First, a new class of data-driven weighting procedures, incorporating group structure and true null proportion estimators, is defined, and its False Discovery Rate (FDR) control is proven asymptotically. This procedure also achieves power optimality under some conditions on the proportion estimators. Secondly, new step-up and step-down procedures, tailored for discrete tests under independence, are designed to control the FDR for arbitrary p-value null marginals. Finally, new confidence bounds for post hoc inference (called post hoc bounds), tailored for the case where the signal is localized, are studied, and the associated optimal post hoc bounds are derived with a simple algorithm.
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Guillermo Durand. Multiple testing and post hoc bounds for heterogeneous data. Statistics [math.ST]. Sorbonne Université, 2018. English. ⟨NNT : 2018SORUS289⟩. ⟨tel-02374758⟩

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