This paper considers Bayesian inference for the partially linear model. Our approach exploits a parametrization of the regression function that is tailored toward estimating a low-dimensional parameter of interest. The key property of the parametrization is that it generates a Neyman orthogonal moment condition meaning that the low-dimensional parameter is less sensitive to the estimation of nuisance parameters. Our large sample analysis supports this claim. In particular, we derive sufficient conditions under which the posterior for the low-dimensional parameter contracts around the truth at the parametric rate and is asymptotically normal with a variance that coincides with the semiparametric efficiency bound. These conditions allow for a larger class of nuisance parameters relative to the original parametrization of the regression model. Overall, we conclude that a parametrization that embeds Neyman orthogonality can be a useful device for debiasing posterior distributions in semiparametric models.

翻译：本文研究部分线性模型的贝叶斯推断。我们的方法利用了针对低维感兴趣参数估计量身定制的回归函数参数化方法。该参数化的关键特性在于能够生成奈曼正交矩条件，使得低维参数对干扰参数估计的敏感度降低。我们的样本分析支持这一结论。具体而言，我们推导了充分条件，在此条件下低维参数的后验分布以参数速率收缩至真实值，且渐近正态性的方差与半参数效率界一致。这些条件允许干扰参数相对于回归模型原始参数化具有更大的类别。总体而言，我们得出结论：嵌入奈曼正交性的参数化方法可成为半参数模型中后验分布去偏的有效工具。