  A popular method for variance reduction in observational causal inference is
propensity-based trimming, the practice of removing units with extreme
propensities from the sample. This practice has theoretical grounding when the
data are homoscedastic and the propensity model is parametric (Yang and Ding,
2018; Crump et al. 2009), but in modern settings where heteroscedastic data are
analyzed with non-parametric models, existing theory fails to support current
practice. In this work, we address this challenge by developing new methods and
theory for sample trimming. Our contributions are three-fold: first, we
describe novel procedures for selecting which units to trim. Our procedures
differ from previous work in that we trim not only units with small
propensities, but also units with extreme conditional variances. Second, we
give new theoretical guarantees for inference after trimming. In particular, we
show how to perform inference on the trimmed subpopulation without requiring
that our regressions converge at parametric rates. Instead, we make only
fourth-root rate assumptions like those in the double machine learning
literature. This result applies to conventional propensity-based trimming as
well and thus may be of independent interest. Finally, we propose a
bootstrap-based method for constructing simultaneously valid confidence
intervals for multiple trimmed sub-populations, which are valuable for
navigating the trade-off between sample size and variance reduction inherent in
trimming. We validate our methods in simulation, on the 2007-2008 National
Health and Nutrition Examination Survey, and on a semi-synthetic Medicare
dataset and find promising results in all settings.
