Before revision:  This is in contrast to other recently proposed methods for solving conditional moment problems based on adversarial machine learning, which do not incorporate optimal weighting, do not establish asymptotic normality, and are not semiparametrically efficient  .
After revision:  This is in contrast to other recently proposed methods for solving conditional moment problems based on adversarial machine learning, which do not incorporate optimal weighting, do not establish asymptotic normality, and are not semiparametrically efficient . In addition, we provide corresponding inference algorithms based on the same kind of variational reformulations, both for kernel- and neural net-based varieties. Finally, we demonstrate the strong performance of our proposed estimation and inference algorithms in a detailed series of synthetic experiments .