Abstract In this talk, we will focus on drawing inferences for average treatment effect type quantities arising in the context of many observational studies. In the first part of the talk, we will try to understand the problem's subtleties in low-dimensional nonparametric settings and discuss the potential usefulness of higher-order semiparametric theory to paint a detailed picture. In another half of the talk, we will consider high-dimensional aspects of the question and discuss different regimes and associated subtleties that arise…