Bayesian Robust Multivariate Linear Regression With Incomplete Data
本文提出一种贝叶斯方法，利用多元t分布等稳健分布处理含缺失数据的多元线性回归，通过单调数据增广算法进行参数估计和缺失值插补。
Abstract The multivariate t distribution and other normal/independent multivariate distributions, such as the multivariate slash distribution and the multivariate contaminated distribution, are used for robust regression with complete or incomplete data. Most previous work focused on the method of maximum likelihood estimation for linear regression using normal/independent distributions. This article considers Bayesian estimation of multivariate linear regression models using normal/independent distributions with fully observed predictor variables and possible missing values from outcome variables. A monotone data augmentation algorithm for posterior simulation of the parameters and missing data imputation is presented. The posterior distributions of functions of the parameters can be obtained using Monte Carlo methods. The monotone data augmentation algorithm can also be used for creating multiple imputations for incomplete data sets. An illustrative example of using the multivariate t is also included.