On empirical distribution function of high-dimensional Gaussian vector components with an application to multiple testing

DOI10.3150/14-BEJ659zbMath1332.62057arXiv1210.2489OpenAlexW2952829715MaRDI QIDQ5963502

Etienne Roquain, Sylvain Delattre

Publication date: 22 February 2016

Published in: Bernoulli (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1210.2489

zbMATH Keywords

functional central limit theoremHermite polynomialsempirical distribution functionfalse discovery ratefactor modelfunctional delta methodGaussian triangular arrayssample correlation matrix

Mathematics Subject Classification ID

Asymptotic distribution theory in statistics (62E20) Functional limit theorems; invariance principles (60F17) Paired and multiple comparisons; multiple testing (62J15)

Related Items (10)

On correlated \(z\)-values distribution in hypothesis testing ⋮ Estimating minimum effect with outlier selection ⋮ Estimating the proportion of signal variables under arbitrary covariance dependence ⋮ A central limit theorem for the Benjamini-Hochberg false discovery proportion under a factor model ⋮ Controlling the false discovery exceedance for heterogeneous tests ⋮ A strong law of large numbers for simultaneously testing parameters of Lancaster bivariate distributions ⋮ A strong law of large numbers related to multiple testing normal means ⋮ On empirical distribution function of high-dimensional Gaussian vector components with an application to multiple testing ⋮ Adaptive \(p\)-value weighting with power optimality ⋮ New procedures controlling the false discovery proportion via Romano-Wolf's heuristic

Uses Software

• FAMT
• leapp

Cites Work

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• On the false discovery proportion convergence under Gaussian equi-correlation
• Limit of the smallest eigenvalue of a large dimensional sample covariance matrix
• An empirical central limit theorem for dependent sequences
• The empirical process of some long-range dependent sequences with an application to U-statistics
• Dependence in probability and statistics
• More powerful control of the false discovery rate under dependence
• The positive false discovery rate: A Bayesian interpretation and the \(q\)-value
• On the distribution of the largest eigenvalue in principal components analysis
• The control of the false discovery rate in multiple testing under dependency.
• Asymptotics of weighted empirical processes of linear fields with long-range dependence
• A stochastic process approach to false discovery control.
• Limit theorems for nonlinear functionals of a stationary Gaussian sequence of vectors
• The empirical process of a short-range dependent stationary sequence under Gaussian subordination
• Moment bounds and central limit theorems for Gaussian subordinated arrays
• Multiple hypothesis testing adjusted for latent variables, with an application to the AGEMAP gene expression data
• Asymptotic properties of false discovery rate controlling procedures under independence
• Exact calculations for false discovery proportion with application to least favorable configura\-tions
• Weak convergence of probabilities on nonseparable metric spaces and empirical measures on Euclidean spaces
• A Factor Model Approach to Multiple Testing Under Dependence
• The effect of correlation in false discovery rate estimation
• Asymptotic Statistics
• Empirical Bayes Analysis of a Microarray Experiment
• Estimating False Discovery Proportion Under Arbitrary Covariance Dependence
• Some Results on the Control of the False Discovery Rate under Dependence
• Heuristic Approach to the Kolmogorov-Smirnov Theorems
• Justification and Extension of Doob's Heuristic Approach to the Kolmogorov- Smirnov Theorems
• Moment bounds and central limit theorem for functions of Gaussian vectors
• On empirical distribution function of high-dimensional Gaussian vector components with an application to multiple testing

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