A Class of Sequential Conditional Probability Ratio Tests
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一类序贯条件概率比检验
- 研究问题
- 如何设计序贯及组序贯检验，在保持接近固定样本检验功效的同时，限制最大样本量并减少平均样本量？
- 方法与思路
- 作者提出 SCPRT，通过控制随机桥在停止边界上的吸收概率确定偏离因子，并由此构造组序贯检验。
- 材料陈述的贡献
- 摘要称，其最大样本量不超过参考固定样本检验，平均样本量效率接近 SPRT，且两者决策不一致概率很小。
- 阅读关注点
- 应核对功效接近与决策一致性的具体定义、边界参数选择，以及组大小灵活性和样本量性质成立的条件。
- 阅读边界
- 仅据 OpenAlex 索引摘要，稿件版本未注明；技术讨论主要限于二值分布，不能把示例结论直接推广至任意分布。
原文摘要
A new class of sequential testing procedures, sequential conditional probability ratio tests (SCPRT's), is proposed. These procedures have the property of having a maximum sample size no larger than a fixed-sample test with an almost identical power function. The efficiency of the SCPRT, in terms of expected sample size, is close to that of Wald's SPRT. Group sequential testing procedures derived from the SCPRT are not restricted to the choices of group sizes and number of groups. At the same time, the SCPRT, the group-SCPRT, and the reference fixed sample size test (RFSST) are agreeable in the sense of having very small probability of leading to different rejection/acceptance results. For the SCPRT or the group-SCPRT, stopping boundaries are decided by appropriate deflection factors determined by controlling absorption probabilities of a random bridge on the SCPRT boundaries. In this article the basic idea for the SCPRT is introduced in a general setup. But examples and technical discussions are restricted mainly to dichotomous distributions, in which the power functions and expected sample sizes for the sequential procedures can be easily computed by a method developed by Xiong.