🤖 AI Summary
This paper addresses complex causal problems—such as interference—that resist conventional experimental design, by proposing a unified functional-space framework for causal inference. Methodologically, it systematically introduces the Riesz representation theorem for the first time in this context, modeling causal effects as linear functionals on potential outcome functions and encoding prior assumptions via the structure of function spaces. This enables principled, unified modeling across diverse causal settings. Theoretically, the paper establishes necessary and sufficient conditions for unbiasedness, consistency, and asymptotic normality of the proposed estimators. Computationally, it constructs a new class of estimators with rigorous statistical guarantees and provides a computable conservative variance estimator, enabling reliable confidence interval construction. Overall, the framework furnishes a rigorous functional-analytic foundation for design-driven causal inference.
📝 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.
