分野別セミナー

Abstract: The classical causal inference 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 i.i.d. copies of (R, RY, Z') are observed. Here, 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 Z. Root-n consistent and asymptotically semiparametrically efficient estimators have already been proposed in the literature. However, we will explore in details the limitation of this type of estimators in terms of their robustness and will show that in certain scenarios where the model is slightly misspecified, they tend to perform poorly. In particular, if the assumption about R and Y being independent is not exactly satisfied, the estimators tend to show very bad performances. Using the theory of rho-estimation, a new robust estimator is therefore proposed. We then show its nonasymptotic behavior under contamination and general misspecification, showing that the approximation error will be close to the nonparametric minimax rate at worst. Then, the root-n consistency of the estimator when the model is correctly specified is studied.