Robust Inference Using Inverse Probability Weighting

By Xinwei Ma, Jingshen Wang. 2018

111 citations recorded by the source corpus.

Abstract Inverse probability weighting (IPW) is widely used in empirical work in economics and other disciplines. As Gaussian approximations perform poorly in the presence of “small denominators,” trimming is routinely employed as a regularization strategy. However, ad hoc trimming of the observations renders usual inference procedures invalid for the target estimand, even in large samples. In this article, we first show that the IPW estimator can have different (Gaussian or non-Gaussian) asymptotic distributions, depending on how “close to zero” the probability weights are and on how large the trimming threshold is. As a remedy, 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, by adapting to these different asymptotic distributions. This robustness is achieved by employing resampling techniques and by correcting a non-negligible trimming bias. We also propose an easy-to-implement method for choosing the trimming threshold by minimizing an empirical analogue of the asymptotic mean squared error. In addition, we show that our inference procedure remains valid with the use of a data-driven trimming threshold. We illustrate our method by revisiting a dataset from the National Supported Work program. Supplementary materials for this article are available online.

Subfields: Statistics and Probability

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In Statistics and Probability

1. Tengyuan Liang
2. Sanjog Misra
3. Max H. Farrell
4. Jing Gao
5. Aidong Zhang
6. Zhixuan Chu
7. Yaliang Li
8. Sheng Li

Citations in the corpus

• Deep Neural Networks for Estimation and Inference: Application to Causal Effects and Other Semiparametric Estimands (2018, methodology): “It may also be possible to employ recently developed extensions to doubly robust estimation (Tan, 2018) and inverse weighting (Ma and Wang, 2018), which may be beneficial in applications.”
• A Survey on Causal Inference (2020, background): “yed as a regularization strategy, which eliminates the samples whose propensity scores are less than a pre-defined threshold [73]. However, this approach is highly sensitive to the amount of trimming [82]. Also, theoretical results in [82] show that the small probability of propensity scores and the”