Doubly-robust and heteroscedasticity-aware sample trimming for causal inference

TL;DR

This paper introduces new methods for sample trimming in causal inference that account for heteroscedasticity and provide valid inference without requiring parametric convergence rates, improving variance reduction techniques.

Contribution

It develops novel trimming procedures that consider both propensity scores and conditional variances, along with theoretical guarantees and bootstrap methods for valid inference in heteroscedastic settings.

Findings

Improved variance reduction in causal inference through heteroscedasticity-aware trimming.

Theoretical guarantees for inference under non-parametric, heteroscedastic models.

Validated methods on real and semi-synthetic datasets showing promising results.

Abstract

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.