Robust Inference Using Inverse Probability Weighting

• 成果类型: Article
• 署名作者: Ma, Xinwei; Wang, Jingshen
• 署名单位: University of California System; University of California San Diego; University of California System; University of California Berkeley
• 刊物名称: JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION
• ISSN/ISSBN: 0162-1459
• DOI: 10.1080/01621459.2019.1660173
• 发表日期: 2020
• 页码: 1851-1860
• 关键词: Bootstrap

摘要

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. for this article are available online.