ROBUSTNESS OF MULTIPLE TESTING PROCEDURES AGAINST DEPENDENCE
ROBUSTNESS OF MULTIPLE TESTING PROCEDURES AGAINST DEPENDENCE
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DOI：
10.1214/07-aos557
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发表时间：
2009-02-01
影响因子：
4.5
通讯作者：
Hall, Peter
中科院分区：
文献类型：
--
作者：
Clarke, Sandy;Hall, Peter
多重假设检验的一个重要方面是控制显着性水平或 I 类错误的水平。当检验统计数据不独立时，在不采取非常保守的程序的情况下处理这个问题可能会特别具有挑战性。在本文中，我们表明，在测试数量通常非常大的当代多重测试问题的背景下，依赖造成的困难没有经典情况那么严重。当检验统计量的零分布相对轻尾时尤其如此，例如，当它们可以基于正态或学生 t 近似时。在那里，如果检验统计数据可以公平地被视为由线性过程生成，那么随着假设数量的不同，基于错误的独立性假设的分析是渐近正确的。特别是，代表出现统计显着性检验结果的指标的零分布的点过程近似为泊松分布，就像独立性的情况一样。泊松过程也具有与独立情况相同的平均值，并且当然没有表现出错误发现的聚集。但是，如果零分布特别重尾，则此结果可能会失败。即使原假设是正确的，也可能会出现具有统计显着性的结果簇。我们对轻尾和重尾情况下的这些不同属性给出了直观的解释，并提供了支持直觉的严格理论。
An important aspect of multiple hypothesis testing is controlling the significance level, or the level of Type I error. When the test statistics are not independent it can be particularly challenging to deal with this problem, without resorting to very conservative procedures. In this paper we show that, in the context of contemporary multiple testing problems, where the number of tests is often very large, the difficulties caused by dependence are less serious than in classical cases. This is particularly true when the null distributions of test statistics are relatively light-tailed, for example, when they can be based on Normal or Student's t approximations. There, if the test statistics can fairly be viewed as being generated by a linear process, an analysis founded on the incorrect assumption of independence is asymptotically correct as the number of hypotheses diverges. In particular, the point process representing the null distribution of the indices at which statistically significant test results occur is approximately Poisson, just as in the case of independence. The Poisson process also has the same mean as in the independence case, and of course exhibits no clustering of false discoveries. However, this result can fail if the null distributions are particularly heavy-tailed. There clusters of statistically significant results can occur, even when the null hypothesis is correct. We give an intuitive explanation for these disparate properties in light- and heavy-tailed cases, and provide rigorous theory underpinning the intuition.