Abstract In this article, we study the causal inference problem with a continuous treatment variable using propensity score-based methods. For a continuous treatment, the generalized propensity score is defined as the conditional density of the treatment-level given covariates (confounders). The...

Abstract An important goal in causal inference is to achieve balance in the covariates among the treatment groups. In this article, we introduce the concept of distributional balance preserving which requires the distribution of the covariates to be the same in different treatment groups. We...

Abstract A powerful tool for the analysis of nonrandomized observational studies has been the potential outcomes model. Utilization of this framework allows analysts to estimate average treatment effects. This article considers the situation in which high-dimensional covariates are present and...

Recently, a class of machine learning-inspired procedures, termed kernel machine methods, has been extensively developed in the statistical literature. In this note, we construct a so-called ‘adaptively minimax’ kernel machine. Such a construction highlights the limits on the...