Simultaneous Critical Values For T-Tests In Very High Dimensions.
Simultaneous Critical Values For T-Tests In Very High Dimensions.
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DOI：
10.3150/10-bej272
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发表时间：
2011-02
期刊：
影响因子：
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通讯作者：
Kosorok MR
中科院分区：
文献类型：
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作者：
Cao H;Kosorok MR
本文考虑了使用t检验的多假设检验问题。假设观察到的数据是独立生成的条件下的基础和未知的两个状态隐藏模型。我们提出了一个渐近有效的数据驱动的过程中找到临界值的拒绝区域控制k-族明智的错误率（k-FWER），错误发现率（FDR）和错误发现比例的尾部概率（FDTP）通过使用单样本和双样本的t-统计量。我们只需要有限的四阶矩加上一些非常一般的条件的平均值和方差的人口凭借中偏差性质的t-统计量。提出了一种新的备择假设比例的相合估计量。模拟研究支持我们的理论结果，并表明，功率的多个测试程序可以大大提高直接使用临界值，而不是传统的p值的方法。我们的方法是应用在分析的微阵列数据从白血病癌症的研究，涉及同时测试大量的假设。
This article considers the problem of multiple hypothesis testing using t-tests. The observed data are assumed to be independently generated conditional on an underlying and unknown two-state hidden model. We propose an asymptotically valid data-driven procedure to find critical values for rejection regions controlling k-family wise error rate (k-FWER), false discovery rate (FDR) and the tail probability of false discovery proportion (FDTP) by using one-sample and two-sample t-statistics. We only require finite fourth moment plus some very general conditions on the mean and variance of the population by virtue of the moderate deviations properties of t-statistics. A new consistent estimator for the proportion of alternative hypotheses is developed. Simulation studies support our theoretical results and demonstrate that the power of a multiple testing procedure can be substantially improved by using critical values directly as opposed to the conventional p-value approach. Our method is applied in an analysis of the microarray data from a leukemia cancer study that involves testing a large number of hypotheses simultaneously.