Estimating the false discovery rate using the stochastic approximation algorithm

• Published in: Biometrika Vol. 95; no. 4; pp. 961 - 977
• Main Authors: Liang, Faming, Zhang, Jian
• Format: Journal Article
• Language: English
• Published: Oxford Oxford University Press 01.12.2008; Biometrika Trust, University College London; Oxford University Press for Biometrika Trust; Oxford Publishing Limited (England)
• Series: Biometrika
• Subjects: Algorithms; Applications; Approximation; Bayesian analysis; Biology, psychology, social sciences; Correlations; Data analysis; Datasets; Density estimation; Ensemble averaging; Estimation methods; Estimators; Exact sciences and technology; False discovery rate; General topics; Hypotheses; Hypothesis testing; Mathematics; Methods; Microarray data analysis; Monte Carlo simulation; Multiple hypothesis testing; Normal distribution; Null hypothesis; P values; Parametric inference; Probability and statistics; Sciences and techniques of general use; Scientific method; Sequential methods; Statistics; Stochastic approximation; Stochastic models; Studies; Test scores; False discovery rate; Microarray data analysis; Stochastic approximation; Ensemble averaging; Multiple hypothesis testing; Biometrics; Density estimation; Averaging method; Score test; Test statistic; Independence; Multiple test; Non parametric estimation; Statistical estimation; Numerical method; Approximation algorithm; Multivariate analysis; Statistical method; Hypothesis test; Statistical test; Sequential method
• ISSN: 0006-3444; 1464-3510
• DOI: 10.1093/biomet/asn036

Testing of multiple hypotheses involves statistics that are strongly dependent in some applications, but most work on this subject is based on the assumption of independence. We propose a new method for estimating the false discovery rate of multiple hypothesis tests, in which the density of test scores is estimated parametrically by minimizing the Kullback-Leibler distance between the unknown density and its estimator using the stochastic approximation algorithm, and the false discovery rate is estimated using the ensemble averaging method. Our method is applicable under general dependence between test statistics. Numerical comparisons between our method and several competitors, conducted on simulated and real data examples, show that our method achieves more accurate control of the false discovery rate in almost all scenarios.