Before revision:  A common problem in this literature is a regression problem with bracketed (interval-censored) outcome variable Y, which creates a set-identified parameter of interest. The recent studies have only considered finite-dimensional linear regression in such context. To incorporate more complex controls into the problem, we consider a partially linear projection of Y on the set functions that are linear in treatment/policy variables and nonlinear in the controls. We characterize the identified set for the linear component of this projection and propose an estimator of its support function.
After revision:  A common problem in this literature is a regression problem with bracketed (interval-censored) outcome variable Y, which creates a set-identified linear models with high-dimensional covariates where the model selection is based on modern machine learning tools. I characterize the boundary (i.e, support function) of the linear component of this projection and propose an estimator of its support function.