Entropy Balancing is Doubly Robust

By Qingyuan Zhao, Daniel Percival. 2015

392 citations recorded by the source corpus.

Abstract Covariate balance is a conventional key diagnostic for methods estimating causal effects from observational studies. Recently, there is an emerging interest in directly incorporating covariate balance in the estimation. We study a recently proposed entropy maximization method called Entropy Balancing (EB), which exactly matches the covariate moments for the different experimental groups in its optimization problem. We show EB is doubly robust with respect to linear outcome regression and logistic propensity score regression, and it reaches the asymptotic semiparametric variance bound when both regressions are correctly specified. This is surprising to us because there is no attempt to model the outcome or the treatment assignment in the original proposal of EB. Our theoretical results and simulations suggest that EB is a very appealing alternative to the conventional weighting estimators that estimate the propensity score by maximum likelihood.

Subfields: Statistics and Probability

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Statistics and Probability

Citations in the corpus

Approximate residual balancing: debiased inference of average treatment effects in high dimensions (2016, background): “(2012, 2016), Hainmueller (2012), Imai and Ratkovic (2014) and Zubizarreta (2015). Our paper is structured as follows.”
Generalized Optimal Matching Methods for Causal Inference (2016, background): “[51] Zhao Qingyuan and Percival Daniel.”
Covariate balancing propensity score by tailored loss functions (2016, methodology): “This fact was noticed in Zhao and Percival [50], Athey et al.”
Matching for Balance (2019, methodology): “The second observation is the connection between matching for balance and covariate balancing weights (Hainmueller 2012, Imai and Ratkovic 2014, Zubizarreta 2015, Chan et al. 2016, Fan et al. 2016, Zhao and Percival 2017, Zhao 2019, Wang and Zubizarreta 2017).”
Minimal dispersion approximately balancing weights: asymptotic properties and practical considerations (2017, methodology): “Again as special cases, stable balancing weights have h(x)= ( 1 n − 1 r −x)(2) and entropy balancing has h(x)= ( 1 n − x) log( 1 n − x). The problem is now in the form of Tseng & Bertsekas (1987) and Tseng and Bertsekas (1991).”
Asymptotic inference of causal effects with observational studies trimmed by the estimated propensity scores (2018, methodology): “Even without sample trimming, the augmented weighting estimator is different from the existing estimators in the literature (e.g., Mercatanti & Li, 2014; Shinozaki & Matsuyama, 2015; Zhao & Percival, 2017).”