A stochastic process approach to false discovery control

By Christopher R. Genovese, Larry A. Wasserman. 2004

464 citations recorded by the source corpus.

This paper extends the theory of false discovery rates (FDR) pioneered by Benjamini and Hochberg [J. Roy. Statist. Soc. Ser B 57 (1995) 289-300]. We develop a framework in which the False Discovery Proportion (FDP)-the number of false rejections divided by the number of rejections-is treated as a stochastic process. After obtaining the limiting distribution of the process, we demonstrate the validity of a class of procedures for controlling the False Discovery Rate (the expected FDP). We construct a confidence envelope for the whole FDP process. From these envelopes we derive confidence thresholds, for controlling the quantiles of the distribution of the FDP as well as controlling the number of false discoveries. We also investigate methods for estimating the p-value distribution.

Subfields: Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/da93ccb6024718d850498f53fa6801bc169ce800

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Citations in the corpus

False Discovery Control for Random Fields (2004, methodology): “The false nondiscovery proportion (FNP) was introduced independently by Genovese and Wasserman (2004) and by Sarkar (2002b) as the analog of power in the FDR context.”
Adaptive FDR control under independence and dependence (2007, background): “In addition, some other works (Genovese and Wasserman, 2004; Storey et al., 2004; Finner et al., 2009) have studied the question of adaptivity to the parameter π0 from an asymptotic viewpoint.”
Journal of the American Statistical Association Estimating False Discovery Proportion under Arbitrary Covariance Dependence Estimating False Discovery Proportion under Arbitrary Covariance Dependence (unknown): “See Genovese and Wasserman (2004), Meinshausen (2006), Efron (2007), Friguet, Kloareg, and Causeur (2009), etc.”
Size, power and false discovery rates (2007, background): “11 , − Efron [8, 10] lists four reasons why f 0 might diﬀer from the theoretical null: 0 .”
The Bayes oracle and asymptotic optimality of multiple testing procedures under sparsity (2010, methodology): “The proposed mixture model for Xi is a specific example of the two-groups model, which was discussed in a wider nonparametric context, for example, in [6, 17, 19] and [24].”
Proportion of non‐zero normal means: universal oracle equivalences and uniformly consistent estimators (2008, methodology): “In a sense, our findings in this paper complement with those in Genovese and Wasserman (2004) and Meinshausen and Rice (2006).”
Dependency and false discovery rate: Asymptotics (2007, background): “Moreover, attempts to improve the LSU-procedure and interesting investigations based on asymptotics can be found, for example, in [9, 10] and [16].”
On stepdown control of the false discovery proportion (2006, methodology): “These ideas are extended in Perone Pacifico, Genovese, Verdinelli and Wasserman [11], where in the context of random fields, the number of null hypotheses is uncountable.”
Permutation-based simultaneous confidence bounds for the false discovery proportion (2018, methodology): “There we also prove that the method of Goeman and Solari (2011) is equivalent to that in Genovese and Wasserman (2004, 2006).”
Estimation of a two‐component mixture model with applications to multiple testing (2012, methodology): “Genovese and Wasserman (2004) used a constant bounding function, δ.t/ = 1, with ηn, β = √{log.2=β/=.2n/}, whereas Meinshausen and Rice (2006) suggested a class of bounding functions but observed that the standard deviation proportional bounding function δ.t/ = √{t.1− t/} has optimal properties…”
Generalizations of the familywise error rate (2005, methodology): “For example, Genovese and Wasserman [3] study asymptotic procedures that control the FDP (and the FDR) in the framework of a random effects mixture model.”
To How Many Simultaneous Hypothesis Tests Can Normal, Student's t or Bootstrap Calibration Be Applied? (2006, background): “KEY WORDS: Bonferroni’s inequality; Edgeworth expansion; Genetic data; Large-deviation expansion; Level accuracy; Microarray data; Quantile estimation; Skewness; Student’s t statistic.”
Exact calculations for false discovery proportion with application to least favorable configurations (2010, background): “Alternatively, some authors are interested in procedures R controlling the FDP, that is, satisfying P[FDP(R) ≤ α] ≥ 1 − γ ; see, for example, [19, 22].”
Semi-Supervised Novelty Detection (2010, background): “…in Section 6, when specified under the above additional conditions, recovers the methodology of nonasymptotic estimation of 1−π which was developed by Genovese and Wasserman (2004), Section 3, and our notion of proper novelty distribution recovers their notion ofpurity in that setting (and has…”
Adapting to unknown sparsity by controlling the false discovery rate (2005, background): “Recent papers have illuminated the FDR from different points of view: asymptotic, Bayesian, empirical Bayes and as the limit of empirical processes [20, 24, 40].”
False discovery and false nondiscovery rates in single-step multiple testing procedures (2006, background): “(5.1) It is also related to the idea of Genovese and Wasserman [8], who suggested using 1 − πθ as a risk function to compare multiple testing procedures.”