Before revision:  In this paper, we propose an inference procedure that is robust not only to small probability weights entering the IPW estimator, but also to a wide range of trimming threshold choices. Our inference procedure employs resampling with a novel bias correction technique. Specifically, we show that both the IPW and trimmed IPW estimators can have different (Gaussian or non-Gaussian) limiting distributions, depending on how "close to zero" the probability weights are and on  the trimming threshold .
After revision:  In this paper, we first show that the IPW estimator can have different (Gaussian or non-Gaussian) limiting distributions, depending on how "close to zero" the probability weights are and on the trimming threshold .