A1106
Title: Robust semiparametric causal inference
Authors: Gaspard Bernard - University of Luxembourg (Luxembourg) [presenting]
Abstract: The problem of estimating the effect of a treatment, assuming that the outcome of the treatment is not necessarily independent of its assignation, is considered. This problem is linked to the semiparametric inference problem consisting of estimating the expectation of $Y$, a Bernoulli random variable, assuming that $\mbox{i.i.d.}$ copies of $(R, RY, {\bf Z}')$ is observed. $R$ is a masking random variable following a Bernoulli distribution, and it is assumed that $R$ and $Y$ are independent conditionally to some vector of covariates ${\bf Z}$. Some root-$n$ consistent and asymptotically semiparametrically efficient estimators have already been proposed in the literature. However, these estimators are not robust. In fact, these estimators rely on fairly strong assumptions about the distribution of $(R,RY, {\bf Z})$, and their performances under contamination could be extremely bad. A new robust estimator is therefore proposed, and both its nonasymptotic behavior under contamination and its root-$n$ consistency when the model is correctly specified are studied.
