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Inference for Batched Adaptive Experiments

Jan Kemper, Davud Rostam-Afschar

arXiv 10 Dec 2025 · Econometrics

arXiv:2512.10156 · PDF · DOI · OpenAlex · Extracted main text

Abstract

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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Most heavily cited references

The works this paper leans on most, across its whole bibliography — not restricted to papers in our corpus. Ranked by composite intensity, which combines how often a work is mentioned, how many sections mention it, and how much of that falls in the main text rather than the appendix.

ReferenceIntensityMentionsSectionsMain text
1Zhang, Kelly and Janson, Lucas and Murphy, Susan (2020) Inference for Batched Bandits1.00053100%
2Hadad, Vitor and Hirshberg, David A. and Zhan, Ruohan and Wager, Ste… (2021) Confidence Intervals for Policy Evaluation in Adaptive Experiments0.64422100%
3Hirano, Keisuke and Porter, Jack R (2025) Asymptotic Representations for Sequential Decisions, Adaptive Experiments, and Batched Bandits0.64422100%
4Avivi, Hadar and Kline, Patrick and Rose, Evan and Walters, Christop… (2021) Adaptive Correspondence Experiments0.40511100%
5Caria, A. Stefano and Gordon, Grant and Kasy, Maximilian and Quinn,… (2023) An Adaptive Targeted Field Experiment: Job Search Assistance for Refugees in Jordan0.40511100%
6Gaul, Johannes J. and Keusch, Florian and Rostam-Afschar, Davud and… (2025) Invitation Messages for Business Surveys: A Multi-Armed Bandit Experiment self0.40511100%
7Hoffmann, M. and Picard, Bertille and Marie, C. and Bied, G (2023) An Adaptive Experiment to Boost Online Skill Signaling and Visibility0.40511100%
8Kasy, Maximilian and Sautmann, Anja (2021) Adaptive Treatment Assignment in Experiments for Policy Choice0.40511100%
9Offer-Westort, Molly and Coppock, Alexander and Green, Donald P (2021) Adaptive Experimental Design: Prospects and Applications in Political Science0.40511100%
10Tabord-Meehan, Max (2023) Stratification Trees for Adaptive Randomisation in Randomised Controlled Trials0.40511100%

Showing the top 10 of 10 scored citations.