提出BOLS方法，解决自适应实验中因果推断的精度不均问题。
Inference for Batched Adaptive Experiments
- 用分批普通最小二乘法聚合各周期处理组与对照组差异。
- 在异方差条件下保持统计检验效力，支持渐近有效置信区间。
- 适合小批次、少周期的自适应实验分析，尤其适用于经济实践。
自适应实验因其优势在经济学及其他领域迅速普及，但给因果推断带来挑战。本文提出一种批处理普通最小二乘（BOLS）检验统计量，用于自适应实验中处理效应的推断。该统计量在异方差条件下实现各周期处理-对照差异的精度均衡聚合，其组合形式为异方差各周期z统计量的标准化平均值，可用于构建渐近有效的置信区间。通过模拟研究比较了典型情形下（周期数少、每批观测数少或多）的拒绝率表现。
原文摘要 · Abstract (English)
The advantages of adaptive experiments have led to their rapid adoption in economics, other fields, as well as among practitioners. However, adaptive experiments pose challenges for causal inference. This note suggests a BOLS (batched ordinary least squares) test statistic for inference of treatment effects in adaptive experiments. The statistic provides a precision-equalizing aggregation of per-period treatment-control differences under heteroskedasticity. The combined test statistic is a normalized average of heteroskedastic per-period z-statistics and can be used to construct asymptotically valid confidence intervals. We provide simulation results comparing rejection rates in the typical case with few treatment periods and few (or many) observations per batch.
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