Sequential experiments achieve i.i.d.-level semiparametric efficiency via an induced average propensity score, attained by batched designs using influence-function regression adjustment or adaptive covariate balancing.
Asymptotic Efficiency Bounds for a Class of Experimental Designs
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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.
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2026 2verdicts
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Semiparametric Efficiency in Sequential Experiments: Characterization and Design via Average Propensity
Sequential experiments achieve i.i.d.-level semiparametric efficiency via an induced average propensity score, attained by batched designs using influence-function regression adjustment or adaptive covariate balancing.