Log-regularly varying scale mixture of normals for robust regression
Log-regularly varying scale mixture of normals for robust regression
复制标题
对数定期变化的正态尺度混合以实现稳健回归
DOI：
10.1016/j.csda.2022.107517
复制
发表时间：
2022
影响因子：
1.8
通讯作者：
Sugasawa Shonosuke
中科院分区：
文献类型：
--
作者：
Hamura Yasuyuki;Irie Kaoru;Sugasawa Shonosuke
对误差分布采用正态分布假设的线性回归可能会由于潜在的离群值而导致回归系数的不希望的后验推断。在本研究中，误差分布被认为是由两个分量组成的有限混合物，一个是薄的，一个是重的。对于重尾分量，引入了一类新的分布；它们的密度是对数规则变化的，并且比柯西分布有更重的尾部。然而，它们被表示为法线的比例混合，这使得在使用Gibbs采样器时能够进行有效的后验推断。在所提出的模型下，利用最小假设集证明了后验分布的稳健性，这证明了在存在异常值的情况下，对系数向量使用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，结果表明，该模型在点估计和区间估计方面的性能得到了改善，计算效率也得到了提高。此外，在回归系数具有收缩先验的实证研究中，证实了该方法的后验稳健性。
Linear regression that employs the assumption of normality for the error distribution may lead to an undesirable posterior inference of regression coefficients due to potential outliers. A finite mixture of two components, one with thin and one with heavy tails, is considered as the error distribution in this study. For the heavily-tailed component, the novel class of distributions is introduced; their densities are log-regularly varying and have heavier tails than the Cauchy distribution. Yet, they are expressed as a scale mixture of normals which enables the efficient posterior inference when using a Gibbs sampler. The robustness of the posterior distributions is proved under the proposed models using a minimal set of assumptions, which justifies the use of shrinkage priors with unbounded densities for the coefficient vector in the presence of outliers. An extensive comparison with the existing methods via simulation study shows the improved performance of the proposed model in point and interval estimation, as well as its computational efficiency. Further, the posterior robustness of the proposed method is confirmed in an empirical study with shrinkage priors for regression coefficients.