3-具有确定性阶段大小和非IID数据的阶段和4阶段测试
3-stage and 4-stage tests with deterministic stage sizes and non-iid data
摘要：
给定一个固定样本量的测试，控制两个特定的，但任意的分布下的错误概率，一个3阶段和两个4阶段的测试建议和分析。对于每一个，一个新的，具体的，非渐近的，非保守的设计，它保证了相同的差错控制作为给定的固定样本量的测试。此外，一阶渐近近似建立在他们的预期样本量下的两个指定的分布，错误概率趋于零。作为推论，它表明，建议的多级测试可以实现，在这个渐近意义下，在这两个分布在类中的所有序贯检验具有相同的差错控制的最佳期望样本量。此外，他们被证明是更强大的Wald的SPRT时，适用于单侧测试问题和控制下的错误概率是足够小的。这些一般性的结果适用于测试问题的iid设置和超越，如测试的相关系数的一阶自回归，或转移阵的有限状态马尔可夫链，并说明在各种数值研究。
英文摘要：
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.
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