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- W4313305264 abstract "Frequentist semiparametric theory has been used extensively to develop doubly robust (DR) causal estimation. DR estimation combines outcome regression (OR) and propensity score (PS) models in such a way that correct specification of just one of two models is enough to obtain consistent parameter estimation. An equivalent Bayesian solution, however, is not straightforward as there is no obvious distributional framework to the joint OR and PS model, and the DR approach involves a semiparametric estimating equation framework without a fully specified likelihood. In this paper, we develop a fully semiparametric Bayesian framework for DR causal inference by bridging a nonparametric Bayesian procedure with empirical likelihood theory via semiparametric linear regression. Instead of specifying a fully probabilistic model, this procedure is only realized through relevant moment conditions. Crucially, this allows the posterior distribution of the causal parameter to be simulated via Markov chain Monte Carlo methods. We show that the posterior distribution of the causal estimator satisfies consistency and the Bernstein–von Mises theorem, when either the OR or PS is correctly specified. Simulation studies suggest that our proposed method is doubly robust and can achieve the frequentist coverage. We also apply this Bayesian method to a real data example to assess the impact of speed cameras on car collisions in England." @default.
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- W4313305264 date "2023-07-01" @default.
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- W4313305264 title "Semiparametric Bayesian doubly robust causal estimation" @default.
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- W4313305264 doi "https://doi.org/10.1016/j.jspi.2022.12.005" @default.
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