Wei G C, Tanner M A
Department of Statistics, Marion Labs, Kansas City, Missouri 64137.
Biometrics. 1991 Dec;47(4):1297-309.
The first part of the article reviews the Data Augmentation algorithm and presents two approximations to the Data Augmentation algorithm for the analysis of missing-data problems: the Poor Man's Data Augmentation algorithm and the Asymptotic Data Augmentation algorithm. These two algorithms are then implemented in the context of censored regression data to obtain semiparametric methodology. The performances of the censored regression algorithms are examined in a simulation study. It is found, up to the precision of the study, that the bias of both the Poor Man's and Asymptotic Data Augmentation estimators, as well as the Buckley-James estimator, does not appear to differ from zero. However, with regard to mean squared error, over a wide range of settings examined in this simulation study, the two Data Augmentation estimators have a smaller mean squared error than does the Buckley-James estimator. In addition, associated with the two Data Augmentation estimators is a natural device for estimating the standard error of the estimated regression parameters. It is shown how this device can be used to estimate the standard error of either Data Augmentation estimate of any parameter (e.g., the correlation coefficient) associated with the model. In the simulation study, the estimated standard error of the Asymptotic Data Augmentation estimate of the regression parameter is found to be congruent with the Monte Carlo standard deviation of the corresponding parameter estimate. The algorithms are illustrated using the updated Stanford heart transplant data set.
本文的第一部分回顾了数据增强算法，并提出了数据增强算法的两种近似方法，用于分析缺失数据问题：穷人数据增强算法和渐近数据增强算法。然后，在删失回归数据的背景下实现这两种算法，以获得半参数方法。在一项模拟研究中检验了删失回归算法的性能。在该研究的精度范围内发现，穷人数据增强估计器和渐近数据增强估计器以及巴克利 - 詹姆斯估计器的偏差似乎都不为零。然而，就均方误差而言，在本模拟研究考察的广泛设置范围内，两种数据增强估计器的均方误差比巴克利 - 詹姆斯估计器更小。此外，与两种数据增强估计器相关联的是一种用于估计估计回归参数标准误差的自然方法。展示了如何使用该方法来估计与模型相关的任何参数（例如，相关系数）的任何一种数据增强估计的标准误差。在模拟研究中，发现回归参数的渐近数据增强估计的估计标准误差与相应参数估计的蒙特卡罗标准差一致。使用更新后的斯坦福心脏移植数据集对算法进行了说明。
