Abstract Manski (Monotone treatment response. Econometrica 1997;65:1311–34) and Manski and Pepper (Monotone instrumental variables: with an application to the returns to schooling. Econometrica 2000;68:997–1010) gave sharp bounds on causal effects under the assumptions of monotone treatment response...

There are many interesting and widely used estimators of a functional with finite semi-parametric variance bound that depend on nonparametric estimators of nuisance func-tions. We use cross-fitting to construct such estimators with fast remainder rates. We give cross-fit doubly robust estimators...

There are many interesting and widely used estimators of a functional with finite semi-parametric variance bound that depend on nonparametric estimators of nuisance func-tions. We use cross-fitting to construct such estimators with fast remainder rates. We give cross-fit doubly robust...