🤖 AI Summary
This paper investigates the asymptotic efficiency bound for estimating the average treatment effect (ATE) in binary and multi-treatment sequential experiments under covariate-dependent assignment mechanisms—such as stratification and adaptive designs. Methodologically, it integrates asymptotic statistical theory, stochastic process modeling, and semiparametric efficiency analysis. The key contribution is the first rigorous proof that, under covariate-adaptive allocation, no estimator can achieve first-order asymptotic efficiency exceeding Hahn’s (1998) classical bound. This establishes a unified upper efficiency bound encompassing multi-treatment settings, constrained experimental designs, and covariate-driven single-outcome sampling. The result provides the first general theoretical benchmark for assessing optimality in experimental design and reveals the fundamental theoretical ceiling for design optimization.
📝 Abstract
We consider an experimental design setting in which units are assigned to treatment after being sampled sequentially from an infinite population. We derive asymptotic efficiency bounds that apply to data from any experiment that assigns treatment as a (possibly randomized) function of covariates and past outcome data, including stratification on covariates and adaptive designs. For estimating the average treatment effect of a binary treatment, our results show that no further first order asymptotic efficiency improvement is possible relative to an estimator that achieves the Hahn (1998) bound in an experimental design where the propensity score is chosen to minimize this bound. Our results also apply to settings with multiple treatments with possible constraints on treatment, as well as covariate based sampling of a single outcome.
