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A Design-Based Riesz Representation Framework for Randomized Experiments

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  • Christopher Harshaw
  • Fredrik Savje
  • Yitan Wang

Abstract

We describe a new design-based framework for drawing causal inference in randomized experiments. Causal effects in the framework are defined as linear functionals evaluated at potential outcome functions. Knowledge and assumptions about the potential outcome functions are encoded as function spaces. This makes the framework expressive, allowing experimenters to formulate and investigate a wide range of causal questions. We describe a class of estimators for estimands defined using the framework and investigate their properties. The construction of the estimators is based on the Riesz representation theorem. We provide necessary and sufficient conditions for unbiasedness and consistency. Finally, we provide conditions under which the estimators are asymptotically normal, and describe a conservative variance estimator to facilitate the construction of confidence intervals for the estimands.

Suggested Citation

  • Christopher Harshaw & Fredrik Savje & Yitan Wang, 2022. "A Design-Based Riesz Representation Framework for Randomized Experiments," Papers 2210.08698, arXiv.org, revised Oct 2022.
    • Handle: RePEc:arx:papers:2210.08698
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    References listed on IDEAS

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    Cited by:

    1. Cortez-Rodriguez Mayleen & Eichhorn Matthew & Yu Christina Lee, 2023. "Exploiting neighborhood interference with low-order interactions under unit randomized design," Journal of Causal Inference, De Gruyter, vol. 11(1), pages 1-36, January.
    2. Michael P. Leung, 2024. "Causal Interpretation of Estimands Defined by Exposure Mappings," Papers 2403.08183, arXiv.org, revised Mar 2024.

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