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Abstract:
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To make inferences based on observational studies, causal inference has received renewed attention and is playing an ever important role in biomedicine and economics. The doubly robust estimator (DRE) is a major advance in this field. However, in practice many outcome measures are functionals of multiple distributions, which can only be estimated via U-statistics and existing DREs do not apply. In this article, we propose a novel class of U-statistic DREs. To further enhance the robustness, we use semiparametric specifications for the propensity score and outcome models in the construction of the U-statistic estimator. Comprehensive asymptotic properties of the proposed estimators are investigated, extensive simulation studies are conducted to evaluate their finite sample behavior and compare with the corresponding parametric U-statistics and the naive estimators, which show significant advantages. Then the method is applied to analyzing real data from the AIDS Clinical Trials Group.
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