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Globally efficient non‐parametric inference of average treatment effects by empirical balancing calibration weighting
Author(s) -
Chan Kwun Chuen Gary,
Yam Sheung Chi Phillip,
Zhang Zheng
Publication year - 2016
Publication title -
journal of the royal statistical society: series b (statistical methodology)
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 6.523
H-Index - 137
eISSN - 1467-9868
pISSN - 1369-7412
DOI - 10.1111/rssb.12129
Subject(s) - estimator , covariate , statistics , mathematics , efficient estimator , weighting , propensity score matching , outcome (game theory) , parametric statistics , econometrics , average treatment effect , inference , score , computer science , minimum variance unbiased estimator , artificial intelligence , medicine , mathematical economics , radiology
Summary The estimation of average treatment effects based on observational data is extremely important in practice and has been studied by generations of statisticians under different frameworks. Existing globally efficient estimators require non‐parametric estimation of a propensity score function, an outcome regression function or both, but their performance can be poor in practical sample sizes. Without explicitly estimating either function, we consider a wide class of calibration weights constructed to attain an exact three‐way balance of the moments of observed covariates among the treated, the control and the combined group. The wide class includes exponential tilting, empirical likelihood and generalized regression as important special cases, and extends survey calibration estimators to different statistical problems and with important distinctions. Global semiparametric efficiency for the estimation of average treatment effects is established for this general class of calibration estimators. The results show that efficiency can be achieved by solely balancing the covariate distributions without resorting to direct estimation of the propensity score or outcome regression function. We also propose a consistent estimator for the efficient asymptotic variance, which does not involve additional functional estimation of either the propensity score or the outcome regression functions. The variance estimator proposed outperforms existing estimators that require a direct approximation of the efficient influence function.