Estimating the Null and the Proportion of Nonnull Effects in Large-Scale Multiple Comparisons

By Jiashun Jin, Tommaso Cai. 2006

219 citations recorded by the source corpus.

An important issue raised by Efron in the context of large-scale multiple comparisons is that in many applications, the usual assumption that the null distribution is known is incorrect, and seemingly negligible differences in the null may result in large differences in subsequent studies. This suggests that a careful study of estimation of the null is indispensable. In this article we consider the problem of estimating a null normal distribution, and a closely related problem, estimation of the proportion of nonnull effects. We develop an approach based on the empirical characteristic function and Fourier analysis. The estimators are shown to be uniformly consistent over a wide class of parameters. We investigate the numerical performance of the estimators using both simulated and real data. In particular, we apply our procedure to the analysis of breast cancer and human immunodeficiency virus microarray datasets. The estimators perform favorably compared with existing methods.

Subfields: Molecular Biology, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/4440efc12b63fd87c8e9336ea39ee35b33d8c1c7

How researchers see this paper

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

In Molecular Biology

In Statistics and Probability

Citations in the corpus

Covariate‐assisted ranking and screening for large‐scale two‐sample inference (2019, methodology): “W. Sun was supported in part by National Science Foundation grants DMS-CAREER-1255406 and DMS-1712983.”
Distribution-free Multiple Testing (2016, background): “There is work in that direction in [7, 21].”
The Bayes oracle and asymptotic optimality of multiple testing procedures under sparsity (2010, methodology): “More sophisticated methods for estimating parameters of the normal null distribution in case of no parametric assumptions on the form of the alternative are provided in [16] and [26].”
Data-driven hypothesis weighting increases detection power in genome-scale multiple testing (2016, methodology): “Note that the authors of [20] suggested using a di↵erent estimator of the local fdr, namely the one in [51].”
PROPERTIES OF HIGHER CRITICISM UNDER STRONG DEPENDENCE (2008, background): “[10], Cai, Jin and Low [4], Genovese and Wasserman [11], Storey, Dai and Leek [26], Jin [18], Jin and Cai [19], Jin, Peng and Wang [21] and Meinshausen and Rice [24]; (3) Donoho and Jin [7], Delaigle and Hall [6], Hall, Pittelkov and Ghosh [12], Ingster [14, 15], Jin [17] and Jager and Wellner [16].”
Multiple Testing for Exploratory Research (2011, methodology): “…in the context of genomic data analysis, and several authors (Schweder and Spjøtvoll, 1982; Benjamini and Hochberg, 2000; Langaas, Lindqvist and Ferkingstad, 2005; Meinshausen and Bühlmann, 2005; Jin and Cai, 2007) have proposed methods for estimating τ(R), although for R= {1, . . . , n} only.”
Oracle and Adaptive Compound Decision Rules for False Discovery Rate Control (2007, methodology): “We report simulation studies in Section 5 demonstrating that the z value–based adaptive procedure is more efﬁcient than the traditional p value–based testing approaches”
Controlling the familywise error rate with plug‐in estimator for the proportion of true null hypotheses (2009, methodology): “Jin and Cai (2007) studied estimation methods that are based on the empirical characteristic function and on Fourier analysis; see also Jin (2008).”
Proportion of non‐zero normal means: universal oracle equivalences and uniformly consistent estimators (2008, methodology): “In fact, if we take ω to be the triangle density, then Theorem 2.4 can be thought as a special case of Theorem 5 in Jin and Cai (2007).”
Asymptotically minimax empirical Bayes estimation of a sparse normal mean vector (2013, methodology): “For example, the sparse normal mean model is the cornerstone for many modern Bayes and empirical Bayes multiple testing procedures, e.g., Scott and Berger (2006), Jin and Cai (2007), Bogdan et al. (2008), Efron (2008), and Martin and Tokdar (2012).”
Adaptive FDR control under independence and dependence (2007, background): “A variety of other estimators of π0 have been proposed (e.g. Meinshausen and Rice, 2006; Jin and Cai, 2007; Jin, 2008); while their asymptotic consistency (as the number of hypotheses tends to infinity) is generally established, their use in plug-in adaptive procedures has not always been studied.”