Journal of the American Statistical Association Estimating False Discovery Proportion under Arbitrary Covariance Dependence Estimating False Discovery Proportion under Arbitrary Covariance Dependence

286 citations recorded by the source corpus.

Multiple hypothesis testing is a fundamental problem in high-dimensional inference, with wide applications in many scientific fields. In genome-wide association studies, tens of thousands of tests are performed simultaneously to find if any single-nucleotide polymorphisms (SNPs) are associated with some traits and those tests are correlated. When test statistics are correlated, false discovery control becomes very challenging under arbitrary dependence. In this article, we propose a novel method—based on principal factor approximation—that successfully subtracts the common dependence and weakens significantly the correlation structure, to deal with an arbitrary dependence structure. We derive an approximate expression for false discovery proportion (FDP) in large-scale multiple testing when a common threshold is used and provide a consistent estimate of realized FDP. This result has important applications in controlling false discovery rate and FDP. Our estimate of realized FDP compares favorably with Efron's approach, as demonstrated in the simulated examples. Our approach is further illustrated by some real data applications. We also propose a dependence-adjusted procedure that is more powerful than the fixed-threshold procedure. Supplementary material for this article is available online.

Subfields: Management Science and Operations Research, Statistics and Probability

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Management Science and Operations Research

In Statistics and Probability

Citations in the corpus

Sufficient Forecasting Using Factor Models (2015, methodology): “…(Fama and French, 1992; Carhart, 1997; Fama and French, 2015; Hou et al., 2015), large-scale multiple testing (Leek and Storey, 2008; Fan et al., 2012), high-dimensional covariance matrix estimation (Fan et al., 2008, 2013), and forecasting using many predictors (Stock and Watson,…”
Data-Driven Market-Making via Model-Free Learning (2020, methodology): “…use any of the three main off-policy evaluation methods: direct method [Bertsekas et al. , 1995; Lagoudakis and Parr, 2003; Sutton and Barto, 2018], importance sampling [Swaminathan and Joachims, 2015], and doubly robust method [Dud´ık et al. , 2014; Jiang and Li, 2015; Robins et al. , 1994].”
SLOPE is Adaptive to Unknown Sparsity and Asymptotically Minimax (2015, methodology): “Having said this, we are aware of recent signiﬁcant progress on this problem including the development of the knockoﬀ ﬁlter [6], which is a powerful FDR controlling method working when p ≤ n , and other innovative ideas [41, 42] relying on assumptions, which may not always hold.”
svaseq: removing batch effects and other unwanted noise from sequencing data (2014, methodology): “For step two of the sva algorithm, estimating latent factors only associated with dependence, it has been proposed to use factor analysis [12], independent components analysis [13], and principal components analysis [14].”
Challenges of Big Data Analysis (2013, background): “We refer to Cai and Jiang (2012) and Fan et al. (2012a) about more theoretical results on characterizing the orders of r . b Let X S = ( X j ) j S be the sub-random vector indexed by S and S the selected set that has the higher spurious correlation with X 1 as in Figure 2.”
PROJECTED PRINCIPAL COMPONENT ANALYSIS IN FACTOR MODELS (2014, unknown): “In calculating the false-discovery proportion for large-scale hypothesis testing, one needs to adjust accurately the common dependence via subtracting it from the data in (1.1) (Leek and Storey, 2008; Friguet et al., 2009; Efron, 2010; Desai and Storey, 2012; Fan et al., 2012).”