论文标题
Gibbs多元分位数的后推断
Gibbs posterior inference on multivariate quantiles
论文作者
论文摘要
贝叶斯和其他基于可能性的方法需要规范统计模型，并且对于未自然定义为模型参数的数量（例如分位数）的推断可能并不完全满意。在本文中，我们为多元分位数构建了一个直接且无模型的Gibbs后部分布。无模型意味着从Gibbs后验提取的推论不存在模型错误指定偏置，而直接意味着不需要关于滋扰参数的先验或边缘化。我们在这里表明，Gibbs后部具有root-$ n $融合率和伯恩斯坦 - 伏米斯（Von Mises）属性，即，对于大N，Gibbs后分布可以由高斯近似。此外，我们提出的数值结果显示了从适当缩放的吉布斯后部得出的可靠集的有效性和效率。
Bayesian and other likelihood-based methods require specification of a statistical model and may not be fully satisfactory for inference on quantities, such as quantiles, that are not naturally defined as model parameters. In this paper, we construct a direct and model-free Gibbs posterior distribution for multivariate quantiles. Being model-free means that inferences drawn from the Gibbs posterior are not subject to model misspecification bias, and being direct means that no priors for or marginalization over nuisance parameters are required. We show here that the Gibbs posterior enjoys a root-$n$ convergence rate and a Bernstein--von Mises property, i.e., for large n, the Gibbs posterior distribution can be approximated by a Gaussian. Moreover, we present numerical results showing the validity and efficiency of credible sets derived from a suitably scaled Gibbs posterior.
