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Efficient Adaptive Experimental Design for Average Treatment Effect Estimation

Author

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  • Masahiro Kato
  • Takuya Ishihara
  • Junya Honda
  • Yusuke Narita

Abstract

The goal of many scientific experiments including A/B testing is to estimate the average treatment effect (ATE), which is defined as the difference between the expected outcomes of two or more treatments. In this paper, we consider a situation where an experimenter can assign a treatment to research subjects sequentially. In adaptive experimental design, the experimenter is allowed to change the probability of assigning a treatment using past observations for estimating the ATE efficiently. However, with this approach, it is difficult to apply a standard statistical method to construct an estimator because the observations are not independent and identically distributed. We thus propose an algorithm for efficient experiments with estimators constructed from dependent samples. We also introduce a sequential testing framework using the proposed estimator. To justify our proposed approach, we provide finite and infinite sample analyses. Finally, we experimentally show that the proposed algorithm exhibits preferable performance.

Suggested Citation

  • Masahiro Kato & Takuya Ishihara & Junya Honda & Yusuke Narita, 2020. "Efficient Adaptive Experimental Design for Average Treatment Effect Estimation," Papers 2002.05308, arXiv.org, revised Oct 2021.
    • Handle: RePEc:arx:papers:2002.05308
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    References listed on IDEAS

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    1. Jinyong Hahn & Keisuke Hirano & Dean Karlan, 2011. "Adaptive Experimental Design Using the Propensity Score," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 29(1), pages 96-108, January.
    2. Keisuke Hirano & Guido W. Imbens & Geert Ridder, 2003. "Efficient Estimation of Average Treatment Effects Using the Estimated Propensity Score," Econometrica, Econometric Society, vol. 71(4), pages 1161-1189, July.
    3. Heejung Bang & James M. Robins, 2005. "Doubly Robust Estimation in Missing Data and Causal Inference Models," Biometrics, The International Biometric Society, vol. 61(4), pages 962-973, December.
    4. Imbens,Guido W. & Rubin,Donald B., 2015. "Causal Inference for Statistics, Social, and Biomedical Sciences," Cambridge Books, Cambridge University Press, number 9780521885881.
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    Cited by:

    1. Shantanu Gupta & Zachary C. Lipton & David Childers, 2021. "Efficient Online Estimation of Causal Effects by Deciding What to Observe," Papers 2108.09265, arXiv.org, revised Oct 2021.

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