  In this paper, we derive a new class of doubly robust estimators for
treatment effect estimands that is also robust against weak covariate overlap.
Our proposed estimator relies on trimming observations with extreme propensity
scores and uses a bias correction device for trimming bias. Our framework
accommodates many research designs, such as unconfoundedness, local treatment
effects, and difference-in-differences. Simulation exercises illustrate that
our proposed tools indeed have attractive finite sample properties, which are
aligned with our theoretical asymptotic results.
