论文标题
对数正常的对数规范的规模混合物，以进行鲁棒回归
Log-Regularly Varying Scale Mixture of Normals for Robust Regression
论文作者
论文摘要
与误差分布的经典正态性假设的线性回归可能导致由于潜在异常值而导致回归系数的后验推断。本文将两个具有薄和重尾部的组件的有限混合物作为误差分布，该分布已常规地用于应用统计。对于大尾部的组件，我们介绍了新颖的分布类别。它们的密度是对数的变化，并且尾巴的尾巴比考奇分布的尾巴更重，但它们表示为正常分布的比例混合物，并可以通过吉布斯采样器进行有效的后验推断。我们证明了在提议的模型下对后验分布的异常值的鲁棒性，其假设集最少，这证明在存在异常值的情况下使用具有无界密度的收缩先验。通过仿真研究与现有方法进行了广泛的比较，显示了我们的模型和间隔估计以及其计算效率的改善。此外，我们在经验研究中证实了我们方法的后鲁棒性，并通过收缩率进行回归系数。
Linear regression with the classical normality assumption for the error distribution may lead to an undesirable posterior inference of regression coefficients due to the potential outliers. This paper considers the finite mixture of two components with thin and heavy tails as the error distribution, which has been routinely employed in applied statistics. For the heavily-tailed component, we introduce the novel class of distributions; their densities are log-regularly varying and have heavier tails than those of Cauchy distribution, yet they are expressed as a scale mixture of normal distributions and enable the efficient posterior inference by Gibbs sampler. We prove the robustness to outliers of the posterior distributions under the proposed models with a minimal set of assumptions, which justifies the use of shrinkage priors with unbounded densities for the coefficient vector in the presence of outliers. The extensive comparison with the existing methods via simulation study shows the improved performance of our model in point and interval estimation, as well as its computational efficiency. Further, we confirm the posterior robustness of our method in the empirical study with the shrinkage priors for regression coefficients.
