Multiple Testing of Composite Null Hypotheses in Heteroscedastic Models

• 成果类型: Article
• 署名作者: Sun, Wenguang; McLain, Alexander C.
• 署名单位: University of Southern California; National Institutes of Health (NIH) - USA; NIH Eunice Kennedy Shriver National Institute of Child Health & Human Development (NICHD)
• 刊物名称: JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION
• ISSN/ISSBN: 0162-1459
• DOI: 10.1080/01621459.2012.664505
• 发表日期: 2012
• 页码: 673-687
• 关键词: false discovery rate; DENSITY-ESTIMATION; gene-expression; EMPIRICAL BAYES; Optimal Rates; P-values; PROPORTION; deconvolution; regression; CONVERGENCE

摘要

In large-scale studies, the true effect sizes often range continuously from zero to small to large, and are observed with heteroscedastic errors. In practical situations where the failure to reject small deviations from the null is inconsequential, specifying an indifference region (or forming composite null hypotheses) can greatly reduce the number of unimportant discoveries in multiple testing. The heteroscedasticity issue poses new challenges for multiple testing with composite nulls. In particular, the conventional framework in multiple testing, which involves resealing or standardization, is likely to distort the scientific question. We propose the concept of a composite null distribution for heteroscedastic models and develop an optimal testing procedure that minimizes the false nondiscovery rate, subject to a constraint on the false discovery rate. The proposed approach is different from conventional methods in that the effect size, statistical significance, and multiplicity issues are addressed integrally. The external information of heteroscedastic errors is incorporated for optimal simultaneous inference. The new features and advantages of our approach are demonstrated using both simulated and real data. The numerical studies demonstrate that our new procedure enjoys superior performance with greater accuracy and better interpretability of results.