Before revision:  We derive finite-sample optimal estimators and confidence intervals (CIs) under the assumption of normal errors when the conditional mean of the outcome variable is constrained only by nonparametric smoothness and/or shape restrictions .
After revision:  We derive finite-sample optimal estimators and confidence intervals (CIs) that are optimal in finite samples when the regression errors are normal with known variance. In contrast to conventional CIs, our CIs use a larger critical value that explicitly takes into account the potential bias of the estimator. When the error distribution is unknown, feasible versions of our CIs are valid asymptotically, even when \sqrt{n the conditional mean of the outcome variable is constrained only by nonparametric smoothness and/or shape restrictions .