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…

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Abstract: In the context of linear regression, we construct a data-driven convex loss function with respect to which empirical risk minimisation yields optimal asymptotic variance in the downstream estimation of the regression coefficients. Our semiparametric approach targets the best decreasing approximation of the derivative of the log-density of the noise distribution. At the population level, this fitting process is a nonparametric extension of score matching, corresponding to a log-concave projection of the noise distribution with respect to the Fisher divergence.…