论文标题
双重稳健的贝叶斯推断平均治疗效果
Double Robust Bayesian Inference on Average Treatment Effects
论文作者
论文摘要
我们提出了一个双重稳健的贝叶斯推论程序，对平均治疗效果（ATE）在不符的情况下提出。对于我们的新贝叶斯方法，我们首先调整条件均值函数的先前分布，然后校正所得ate的后验分布。这两种调整都利用了由半参数影响函数进行ATE估计的动力估计器。我们通过在双重鲁棒性下建立新的半参数Bernstein-von Mises定理来证明贝叶斯程序的渐近等效性和有效的频繁估计量。即，缺乏条件平均功能的平滑度可以通过倾向得分的高规律性来补偿，反之亦然。因此，由此产生的贝叶斯可信集构成置信区间，均不确切的覆盖率概率。在模拟中，我们的方法通过后均值和可靠的间隔提供了与标称覆盖范围概率紧密相一致的后均值和可靠的间隔的精确点估计。此外，与现有方法相比，我们的方法达到了较短的间隔长度。我们在Lalonde [1986]和Dehejia and Wahba [1999]的申请中的应用中说明了我们的方法。
We propose a double robust Bayesian inference procedure on the average treatment effect (ATE) under unconfoundedness. For our new Bayesian approach, we first adjust the prior distributions of the conditional mean functions, and then correct the posterior distribution of the resulting ATE. Both adjustments make use of pilot estimators motivated by the semiparametric influence function for ATE estimation. We prove asymptotic equivalence of our Bayesian procedure and efficient frequentist ATE estimators by establishing a new semiparametric Bernstein-von Mises theorem under double robustness; i.e., the lack of smoothness of conditional mean functions can be compensated by high regularity of the propensity score and vice versa. Consequently, the resulting Bayesian credible sets form confidence intervals with asymptotically exact coverage probability. In simulations, our method provides precise point estimates of the ATE through the posterior mean and credible intervals that closely align with the nominal coverage probability. Furthermore, our approach achieves a shorter interval length in comparison to existing methods. We illustrate our method in an application to the National Supported Work Demonstration following LaLonde [1986] and Dehejia and Wahba [1999].
