论文标题
贝叶斯多元分位数回归先验
Bayesian Multivariate Quantile Regression Using Dependent Dirichlet Process Prior
论文作者
论文摘要
在本文中，我们考虑了一种非参数贝叶斯对多元分位数回归的方法。给定单变量协变量X的响应向量Y的相关条件分布的收集是使用依赖的Dirichlet过程（DDP）进行建模的。 DDP用于跨X引入依赖性。由于先前的Dirichlet过程的实现几乎是离散的，因此我们需要与内核进行卷积。为了尽可能灵活地对误差分布进行建模，我们将多维正常分布的可数混合物作为我们的内核。对于后验计算，我们使用DDP的截断杆破坏的表示。此近似使我们只能处理有限数量的参数。我们使用块Gibbs采样器来估计模型参数。我们通过模拟研究和实际数据应用来说明我们的方法。最后，我们通过后验一致性为提出的方法提供了理论上的理由。即使响应是单变量，我们提出的程序也是新的。
In this article, we consider a non-parametric Bayesian approach to multivariate quantile regression. The collection of related conditional distributions of a response vector Y given a univariate covariate X is modeled using a Dependent Dirichlet Process (DDP) prior. The DDP is used to introduce dependence across x. As the realizations from a Dirichlet process prior are almost surely discrete, we need to convolve it with a kernel. To model the error distribution as flexibly as possible, we use a countable mixture of multidimensional normal distributions as our kernel. For posterior computations, we use a truncated stick-breaking representation of the DDP. This approximation enables us to deal with only a finitely number of parameters. We use a Block Gibbs sampler for estimating the model parameters. We illustrate our method with simulation studies and real data applications. Finally, we provide a theoretical justification for the proposed method through posterior consistency. Our proposed procedure is new even when the response is univariate.
