Inverse-probability-weighted estimator of the average treatment effect (${\widehat{\mathrm{ATE}}}_{\mathrm{IPW}}$)

For binary treatment, outcomes $Y_i$, and estimated propensity score $\hat{e}(X_i)$, the inverse-probability-weighted estimator isIt is consistent under conditional exchangeability, consistency of potential outcomes, positivity in causal inference, and a consistent propensity-score estimator.