Optimal tests following sequential experiments
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序贯实验结束后的最优检验
- 研究问题
- 在抽样决策随实验过程调整的序贯实验结束后，如何刻画检验的渐近功效，并在无偏性或显著性支出限制下构造最优检验？
- 方法与思路
- 作者将检验渐近功效映射到各处理对应的高斯过程极限实验，并利用最终抽样次数及得分或有效影响函数过程终值。
- 材料陈述的贡献
- 摘要称给出固定统计量集合的渐近充分性结果，刻画多种限制下的最优检验，并应用于成本抽样、组序贯和老虎机实验。
- 阅读关注点
- 应核对极限实验与功效匹配的正则条件、允许的序贯分配规则，以及无偏性和显著性支出约束如何改变最优检验。
- 阅读边界
- 所据为 arXiv 预印本，同行评审或期刊接收未经核实；摘要未列渐近框架与有限样本保证，不能据此认定任意实验均适用。
原文摘要
Recent years have seen tremendous advances in the theory and application of sequential experiments. While these experiments are not always designed with hypothesis testing in mind, researchers may still be interested in performing tests after the experiment is completed. The purpose of this paper is to aid in the development of optimal tests for sequential experiments by analyzing their asymptotic properties. Our key finding is that the asymptotic power function of any test can be matched by a test in a limit experiment where a Gaussian process is observed for each treatment, and inference is made for the drifts of these processes. This result has important implications, including a powerful sufficiency result: any candidate test only needs to rely on a fixed set of statistics, regardless of the type of sequential experiment. These statistics are the number of times each treatment has been sampled by the end of the experiment, along with final value of the score (for parametric models) or efficient influence function (for non-parametric models) process for each treatment. We then characterize asymptotically optimal tests under various restrictions such as unbiasedness, α-spending constraints etc. Finally, we apply our our results to three key classes of sequential experiments: costly sampling, group sequential trials, and bandit experiments, and show how optimal inference can be conducted in these scenarios.