置信视界
Confidence Horizons
浏览论文内容
中文总结 AI 辅助
本文提出“置信视界”统计对象，通过放弃有限视界外的有效性，获得更精确的大样本任意时间有效推断，推导了相关统计量的闭式分布函数，可用于处理效应估计。
中文摘要 AI 辅助
任意时间有效的推断方法允许分析人员持续监测数据并提前终止实验，但大多数此类方法在无限时间视界上保持有效性，会产生一定的保守性。在实践中，由于预算、实际或伦理约束，可能会对时间视界施加一个界限。本文提出问题：“通过放弃超过某个有限时间视界的有效性，是否有可能获得更精确的大样本任意时间有效的推断？”我们给出了肯定的答案，方法是提出一类我们称之为“置信视界”的统计对象。这些对象可视为有限时间视界上的大样本置信序列，或等效为具有最大中期窥视次数的组序贯重复置信区间。我们明确了其与 Pocock [1977]、O'Brien--Fleming [1979] 和 Wang--Tsiatis [1987] 的组序贯边界的联系。我们推导了某些统计量的闭式分布函数，可用于精确计算置信视界的渐近分位数，从而避免了组序贯方法中通常采用的重复积分。我们举例说明了置信视界在自适应 Neyman 分配下的序贯随机实验中处理效应估计的应用。
英文摘要
Anytime-valid inference enables analysts to continuously monitor their data and stop experiments early. However, the majority of these methods incur a certain conservativeness by remaining valid on infinite time horizons. In practice, a bound on the horizon may be imposed due to budgetary, practical, or ethical constraints. In this paper, we ask the question: "Is it possible to obtain sharper large-sample anytime-valid inference by forgoing validity beyond some finite time horizon?". We provide a positive answer to this question by proposing a family of statistical objects that we call "confidence horizons". These objects can be viewed as large-sample confidence sequences on bounded time horizons, or alternatively as group sequential repeated confidence intervals with a maximal number of interim peeking times. We make explicit connections to the group sequential boundaries of Pocock [1977], O'Brien--Fleming [1979], and Wang--Tsiatis [1987]. We derive closed-form distribution functions of certain statistics which can be used to calculate the asymptotic quantiles of confidence horizons exactly, sidestepping the repeated integration typically employed in group sequential methods. We illustrate the use of confidence horizons for treatment effect estimation in sequentially randomized experiments under adaptive Neyman allocation.
发表机构
- University of California, Berkeley（加州大学伯克利分校）
机构由 AI 辅助整理，请以论文原文为准。
