Bayesian ridge estimators based on copula-based joint prior distributions for regression coefficients
Bayesian ridge estimators based on copula-based joint prior distributions for regression coefficients
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DOI：
10.1007/s00180-022-01213-8
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发表时间：
2022-03-23
影响因子：
1.3
通讯作者：
Emura, Takeshi
中科院分区：
文献类型：
--
作者：
Michimae, Hirofumi;Emura, Takeshi
岭回归是一种广泛使用的方法，以减轻经常出现在多元线性回归的多重共线性问题。众所周知，岭回归估计可以在多元正态先验下通过后验模式从贝叶斯框架中导出。然而，岭回归模型与Copula为基础的多元先验模型尚未在贝叶斯框架。由于相互作用项的多重共线性问题，我们采用藤copula构造基于copula的联合先验分布。对于选定的Copula和超参数，我们提出了贝叶斯岭估计和可信区间的回归系数。仿真研究进行了比较四种不同的先验（克莱顿，Gumbel和高斯copula先验，和三变量正常的先验）的回归系数的性能。我们的模拟研究表明，阿基米德（克莱顿和Gumbel）Copula先验给出更准确的估计，在多重共线性的存在相比，其他先验。最后，通过对一个真实的数据集的分析，比较了贝叶斯岭估计和一些频率估计。
Ridge regression is a widely used method to mitigate the multicollinearly problem often arising in multiple linear regression. It is well known that the ridge regression estimator can be derived from the Bayesian framework by the posterior mode under a multivariate normal prior. However, the ridge regression model with a copula-based multivariate prior model has not been employed in the Bayesian framework. Motivated by the multicollinearly problem due to an interaction term, we adopt a vine copula to construct the copula-based joint prior distribution. For selected copulas and hyperparameters, we propose Bayesian ridge estimators and credible intervals for regression coefficients. A simulation study is carried out to compare the performance of four different priors (the Clayton, Gumbel, and Gaussian copula priors, and the tri-variate normal prior) on the regression coefficients. Our simulation studies demonstrate that the Archimedean (Clayton and Gumbel) copula priors give more accurate estimates in the presence of multicollinearity compared with the other priors. Finally, a real dataset is analyzed, where the Bayesian ridge estimators and some frequentist estimators are compared.