论文标题
具有确定性阶段尺寸和非IID数据的三阶段和4阶段测试
3-stage and 4-stage tests with deterministic stage sizes and non-iid data
论文作者
论文摘要
给定一个固定样本大小的测试，该测试在两个特定但任意的分布，三阶段和两个4阶段测试下控制误差概率。对于他们每个人，都指定了一种新颖的，具体的，非质子，非保守的设计，该设计保证了与给定的固定样本大小的测试相同的误差控制。此外，随着误差概率为零，在两个规定的分布中，在其预期样本量上建立了一阶渐近近似。作为推论，可以表明，从这种渐近意义上讲，所提出的多阶段测试可以实现所有顺序测试中具有相同误差控制的所有顺序测试的最佳预期样本量。此外，当将它们应用于单方面测试问题时，它们比Wald的SPRT更强大，并且控制的错误概率足够小。这些一般结果应用于IID设置中及以后的测试问题，例如测试一阶自动降低的相关系数，或有限国家马尔可夫链的过渡矩阵，并在各种数值研究中进行了说明。
Given a fixed-sample-size test that controls the error probabilities under two specific, but arbitrary, distributions, a 3-stage and two 4-stage tests are proposed and analyzed. For each of them, a novel, concrete, non-asymptotic, non-conservative design is specified, which guarantees the same error control as the given fixed-sample-size test. Moreover, first-order asymptotic approximation are established on their expected sample sizes under the two prescribed distributions as the error probabilities go to zero. As a corollary, it is shown that the proposed multistage tests can achieve, in this asymptotic sense, the optimal expected sample size under these two distributions in the class of all sequential tests with the same error control. Furthermore, they are shown to be much more robust than Wald's SPRT when applied to one-sided testing problems and the error probabilities under control are small enough. These general results are applied to testing problems in the iid setup and beyond, such as testing the correlation coefficient of a first-order autoregression, or the transition matrix of a finite-state Markov chain, and are illustrated in various numerical studies.
