Estimation and inference based on Neumann series approximation to locally efficient score in missing data problems.
Estimation and inference based on Neumann series approximation to locally efficient score in missing data problems.
复制标题
DOI：
10.1111/j.1467-9469.2009.00646.x
复制
发表时间：
2009-12-01
期刊：
影响因子：
--
通讯作者：
Chen HY
中科院分区：
文献类型：
--
作者：
Chen HY
关于缺失数据问题的半参数有效估计理论已经由Robins和他的合作者系统地发展。除了相对简单的问题外，半参数有效分数不能用封闭形式表示。相反，有效分数通常表示为积分方程的解。在这些情况下，以逐次逼近的形式提出了诺伊曼级数。基于诺伊曼级数近似的估计量的统计性质难以获得，因此尚未得到明确的研究。本文将逐次逼近用简单迭代的形式重新表述，并在此基础上研究了估计量的统计性质。在对似然评分进行鲁棒化的过程中，我们证明了采用该算法可以得到一个双鲁棒的局部有效估计量。结果可以应用于参数回归、边际回归和Cox回归等数据缺失值和缺失数据随机缺失的情况。通过仿真研究对该方法的性能进行了评价，并对一个实际数据实例进行了分析，验证了该方法的有效性。
Theory on semiparametric efficient estimation in missing data problems has been systematically developed by Robins and his coauthors. Except in relatively simple problems, semiparametric efficient scores cannot be expressed in closed forms. Instead, the efficient scores are often expressed as solutions to integral equations. Neumann series was proposed in the form of successive approximation to the efficient scores in those situations. Statistical properties of the estimator based on the Neumann series approximation are difficult to obtain and as a result, have not been clearly studied. In this paper, we reformulate the successive approximation in a simple iterative form and study the statistical properties of the estimator based on the reformulation. We show that a doubly-robust locally-efficient estimator can be obtained following the algorithm in robustifying the likelihood score. The results can be applied to, among others, the parametric regression, the marginal regression, and the Cox regression when data are subject to missing values and the missing data are missing at random. A simulation study is conducted to evaluate the performance of the approach and a real data example is analyzed to demonstrate the use of the approach.
登录
查看更多内容
DOI：
10.1198/016214504000001727
发表时间：
2004-12-01
影响因子：
3.7
作者：
Chen, HY
通讯作者：
Chen, HY
影响因子：
3.7
作者：
Scharfstein, DO;Rotnitzky, A;Robins, JM
通讯作者：
Robins, JM
影响因子：
3.7
作者：
Lipsitz, SR;Ibrahim, JG;Zhao, LP
通讯作者：
Zhao, LP
影响因子：
3.7
作者：
ROBINS, JM;ROTNITZKY, A;ZHAO, LP
通讯作者：
ZHAO, LP
影响因子：
2
作者：
Rotnitzky, A;Robins, J
通讯作者：
Robins, J