Logarithmically efficient simulation for misclassification probabilities in sequential multiple testing
Logarithmically efficient simulation for misclassification probabilities in sequential multiple testing
复制标题
顺序多重测试中误分类概率的对数有效模拟
DOI：
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发表时间：
2016
期刊：
影响因子：
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通讯作者：
Georgios Fellouris
中科院分区：
文献类型：
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作者：
Yanglei Song;Georgios Fellouris
我们考虑通过蒙特卡罗模拟估计两个连续多重测试程序的错误分类概率的问题。当所有本地测试统计数据同时超过正阈值或负阈值时，第一个停止。第二个假设知道信号的真实数量（例如 m），并在前 m 个测试统计数据与其余信号之间的差距超过阈值时停止。对于每个多重测试过程，我们提出了一种重要性采样算法来估计其误分类概率。当各种统计假设的数据是独立的并且每个测试问题满足渐近稳定性条件和对称条件时，这些算法被证明是对数有效的。我们的理论结果通过测试高斯随机游走漂移的特殊情况的模拟研究来说明。
We consider the problem of estimating via Monte Carlo simulation the misclassification probabilities of two sequential multiple testing procedures. The first one stops when all local test statistics exceed simultaneously either a positive or a negative threshold. The second assumes knowledge of the true number of signals, say m, and stops when the gap between the top m test statistics and the remaining ones exceeds a threshold. For each multiple testing procedure, we propose an importance sampling algorithm for the estimation of its misclassification probability. These algorithms are shown to be logarithmically efficient when the data for the various statistical hypotheses are independent, and each testing problem satisfies an asymptotic stability condition and a symmetry condition. Our theoretical results are illustrated by a simulation study in the special case of testing the drifts of Gaussian random walks.