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Abstract:
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A common goal in observational research is to estimate marginal causal effects in the presence of confounding. One solution to this problem is to use the distribution of the covariates to weight the outcomes in such a way to make the data appear as though it were randomized. The propensity score is a natural quantity that arises in this setting. Propensity score weights have appealing asymptotic properties, but they often fail to adequately balance covariate data in finite sample settings. As an alternative, empirical covariate balancing methods have appeared which exactly balance the sample moments of the covariate distribution. With this objective in mind, we propose a framework for estimating covariate balancing weights by solving a constrained convex optimization problem. We use a broad class of functions called Bregman distances as the criterion to be optimized. An interesting byproduct that results from the optimization, called duality, is used to prove asymptotic results for an estimator of the average treatment effect. A series of numerical studies is presented to show how some of the other published covariate balancing methods relate to our framework.
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