Multiple Testing of Composite Null Hypotheses in Heteroscedastic Models
Multiple Testing of Composite Null Hypotheses in Heteroscedastic Models
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DOI：
10.1080/01621459.2012.664505
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发表时间：
2012-05
影响因子：
3.7
通讯作者：
Wenguang Sun;A. McLain
中科院分区：
文献类型：
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作者：
Wenguang Sun;A. McLain
在大规模研究中，真实效应量的范围通常从零到小到大，并且观察到异方差误差。在实际情况下，拒绝与零值的小偏差是无关紧要的，指定一个无差异区域（或形成复合零假设）可以大大减少多重检验中不重要的发现的数量。异方差问题提出了新的挑战，多个测试与复合零。特别是，多重测试中的传统框架，涉及重新缩放或标准化，可能会扭曲科学问题。我们提出了一个复合零分布异方差模型的概念，并制定了一个最佳的测试程序，最大限度地减少了错误的非发现率，受到约束的错误发现率。所提出的方法是不同于传统的方法，在效果大小，统计学意义，和多重性的问题，整体解决。异方差误差的外部信息被纳入最优的同时推理。使用模拟和真实的数据证明了我们的方法的新功能和优势。数值研究表明，我们的新方法具有上级性能与更高的精度和更好的解释性的结果。
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 rescaling 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.