一致可测试性蕴含非对称可测试性
Uniform Testability Implies Asymmetric Testability
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中文总结 AI 辅助
该研究证明了一致固定时间测试到全样本单侧误差控制和一致未来尾控制的过滤级转换，将其应用于有限字母坐标过程，证实了Ryabko猜想5.2的第一个蕴含关系。
中文摘要 AI 辅助
我们证明了一种过滤级转换方法，可将一致固定时间测试转化为全样本单侧误差控制和一致未来尾控制。给定一个自适应确定性二元测试，其最坏情况下的固定时间误差趋于零，该构造方法会选择具有指定可求和误差预算的更新时刻，并在下次更新前保持每个选定的决策。对于每个指定的显著性水平，该构造方法生成的测试可在每个样本量下控制第一类错误；从每个更新时刻起，任意后续误差的概率在每个假设类上被剩余预算一致地界定。因此，该测试是一致收敛的，且在两个假设下几乎必然最终正确。将该转换应用于有限字母坐标过程，可证明Ryabko猜想5.2中的第一个蕴含关系。
英文摘要
We prove a filtration-level conversion from uniform fixed-time testing to all-sample one-sided error control and uniform future-tail control. Given an adapted deterministic binary test whose worst-case fixed-time error tends to zero, the construction selects update times with prescribed summable error budgets and holds each selected decision until the next update. For every prescribed significance level, the construction yields a test that controls Type I error at every sample size; from each update time onward, the probability of any subsequent error is bounded uniformly over each hypothesis class by the remaining budget. Hence the test is uniformly consistent and eventually correct almost surely under both hypotheses. Applying the conversion to finite-alphabet coordinate processes proves the first implication in Ryabko's Conjecture 5.2.
