This paper develops a general framework for conducting inference on the rank of an unknown matrix Π0. A defining feature of our setup is the null hypothesis of the form . The problem is of first-order importance because the previous literature focuses on by implicitly assuming away , which...

In this paper we consider nonparametric estimation of a structural equation model under full additivity constraint. We propose estimators for both the conditional mean and gradient which are consistent, asymptotically normal, oracle efficient and free from the curse of dimensionality. Monte...