Lower bounds for the number of false null hypotheses for multiple testing of associations under general dependence structures

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Proportion of non‐zero normal means: universal oracle equivalences and uniformly consistent estimators (2008, methodology): “Lemma 4.1 implies that Meinshausen and Rice’s estimator (also those in Genovese and Wasserman (2004), Efron et al. (2001), Meinshausen and Bühlmann (2005) and Swanepoel (1999)) is generally not consistent.”
Controlling the familywise error rate with plug‐in estimator for the proportion of true null hypotheses (2009, background): “Meinshausen and Bühlmann (2005) constructed lower bounds for the number of false hypotheses under general dependence and Meinshausen and Rice (2006) proposed a family of methods for establishing a lower confidence bound for the proportion of false null hypotheses under independence.”
Permutation-based simultaneous confidence bounds for the false discovery proportion (2018, methodology): “In Meinshausen and B¨uhlmann (2005) these are referred to as bounding functions.”
False Discovery Control for Multiple Tests of Association Under General Dependence (2006, background): “The estimate m̂1 is in particular equivalent to the estimate in Meinshausen & Bühlmann (2005) under the quantile bounding function.”