A statistical problem that arises in several fields is that of estimating the features of an unknown distribution, which may be conditioned on covariates, using a sample of binomial observations on whether draws from this distribution exceed threshold levels set by experimental design....

Let H 0 (X) be a function that can be nonparametrically estimated. Suppose E [ Y | X ]= F 0 [ X ß 0 H 0 (X) ] . Many models fit this framework, including latent in- dex models with an endogenous regressor and nonlinear models with sample se- lection. We show that the vector ß 0 and unknown...