Asymptotically optimal, sequential, multiple testing procedures with prior information on the number of signals
Asymptotically optimal, sequential, multiple testing procedures with prior information on the number of signals
复制标题
渐进最优、顺序、多重测试程序，具有信号数量的先验信息
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
假设从独立流中依次收集数据，我们考虑在两种一般设置下同时检验多个二元假设；当信号的数量（正确的选择）是已知的，当我们只有一个下限和上限。在这些设置中，我们提出了可行的程序，在没有任何分布假设的情况下，控制类型I和类型II的家庭错误概率低于给定的用户指定水平。然后，在每个流中有i.i.d观测值的情况下，我们证明了所提出的过程在每种可能的信号配置下，随着两个误差概率以任意速率消失，渐近地实现了最佳期望样本量。在完全对称的情况下进行了模拟研究，并支持从我们的渐近结果中获得的见解，例如，与没有先验信息的情况相比，信号的确切数量的知识大约是预期观测数量的一半。
Assuming that data are collected sequentially from independent streams, we consider the simultaneous testing of multiple binary hypotheses under two general setups; when the number of signals (correct alternatives) is known in advance, and when we only have a lower and an upper bound for it. In each of these setups, we propose feasible procedures that control, without any distributional assumptions, the familywise error probabilities of both type I and type II below given, user-specified levels. Then, in the case of i.i.d. observations in each stream, we show that the proposed procedures achieve the optimal expected sample size, under every possible signal configuration, asymptotically as the two error probabilities vanish at arbitrary rates. A simulation study is presented in a completely symmetric case and supports insights obtained from our asymptotic results, such as the fact that knowledge of the exact number of signals roughly halves the expected number of observations compared to the case of no prior information.