Dynamic treatment effects: high-dimensional inference under model misspecification

Statistical inference and estimation for causal relationships has a long tradition and has attracted significant attention as the emerging of large and complex datasets and the need for new statistical tools to handle such challenging datasets. In many applications, data is collected dynamically over time, and individuals are exposed to treatments at multiple stages. Typical examples include mobile health datasets, electronic health records, and many other biomedical studies and political science datasets. This work considers statistical inference of causal effects for longitudinal and observational data with high-dimensional covariates (confounders). We aim to establish valid statistical inference for dynamic treatment effects under possible model misspecifications. For the sake of simplicity, we consider dynamic settings with two exposure times. Suppose that we collect independent and identically distributed (i.i.d.) samples S: (W