Conference Agenda

Estimating some mathematical expectations from partially observed data and in particular missing outcomes is a central problem encountered in numerous fields such as transfer learning, counterfactual analysis or causal inference. Matching estimators, estimators based on k-nearest neighbors, are widely used in this context. Under suitable regularity conditions, one can show that the variance of such estimators can converge to zero at a parametric rate. However their bias can have a slower rate when the dimension of the covariates is larger than 2. This makes analysis of this bias particularly important. In this paper, we provide higher order properties of the bias. In contrast to the existing literature on this topic, we do not assume that the support of the target distribution of the covariates is strictly included in that of the source, and we discuss two geometric conditions on the support that prevent boundary bias issues. We show that these conditions are much more general than the usual convex support assumption, leading to an improvement of existing results. Furthermore, we show that the matching estimator studied by Abadie and Imbens (2006) for the average treatment effect can be asymptotically efficient when the dimension of the covariates is less than 4, a result only known in dimension 1.