Designing Transportable Experiments Under S-admissability

We consider the problem of designing a randomized experiment on a source population to estimate the Average Treatment Effect (ATE) on a target population. Under the covariate shift assumption, we design an unbiased importance-weighted estimator for the target population's ATE. To reduce the variance of our estimator, we design a covariate balance condition between the treatment and control group. Under the rerandomization scheme [Morgan et al., 2012], the experimenter repeatedly rejects a random assignment until it satisfies the condition. We show that when the sample size is large, for a rejection threshold $\alpha$, our balance condition achieves the optimal variance reduction.