Robust semiparametric causal inference

• Mathematics Department, University of Luxembourg, Esch-sur-Alzette, Luxembourg [gaspard.bernard@uni.lu]

Keywords: Causal inference – Robust inference – Semiparametric inference – Estimation of a functional

1 Abstract

In this talk, we consider the problem of estimating the effect of a treatment, assuming that this treatment has not been randomly assigned to patients. More precisely, we consider the problem of estimating $\mathrm{E}(Y)$ with $Y$ a Bernoulli random variable, under the assumption that we observe i.i.d. copies of $(R,RY,𝐙)$. Here, $R$ is a masking random variable, following a Bernoulli distribution and independent of $Y$ conditionally to some vector of covariates $𝐙$. This problem has been studied in a frequentist framework in Robins et al. [2017] and in a bayesian framework in Ray and van der Vaart [2020], where some root-$n$ consistent and asymptotically semiparametrically efficient estimators have been proposed. However, these estimators are not robust. In fact, these estimators rely on fairly strong assumptions about the distribution of $(R,RY,𝐙)$ and their performances under contamination could be extremely bad. We therefore propose a new robust estimator and study both its nonasymptotic behaviour under contamination as well as its root-$n$ consistency when the model is correctly specified.