Identification and Estimation of the Probabilities of Potential Outcome Types Using Covariate Information in Studies with Non-compliance

We propose novel identification conditions and a statistical estimation method for the probabilities of potential outcome types using covariate information in randomized trials which treatment assignment is but subject compliance not perfect. Different from existing studies, proposed do require strict assumptions such as assumption monotonicity. When are identifiable through conditions, problem estimating reduced to that singular models. Thus, cannot be evaluated standard likelihood-based methods. Rather, show we can derive consistent estimators via moments, leads asymptotic normality delta under regular conditions. also new based on bounded constrained augmented Lagrangian more efficient than derived moments.