Using EM to Obtain Asymptotic Variance-Covariance Matrices: The SEM Algorithm
Using EM to Obtain Asymptotic Variance-Covariance Matrices: The SEM Algorithm
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DOI：
10.1080/01621459.1991.10475130
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发表时间：
1991-12
影响因子：
3.7
通讯作者：
X. Meng;D. Rubin
中科院分区：
文献类型：
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作者：
X. Meng;D. Rubin
摘要期望最大化（EM）算法是不完全数据问题中最大似然估计的一种常用且非常简单的方法。EM在实践中的一个批评是，参数的渐近方差-协方差矩阵（例如，标准误差）不是自动的副产品，因为它们是在使用一些其他方法时，如牛顿-拉夫森。在这篇文章中，我们定义并说明了一个程序，获得数值稳定的渐近方差-协方差矩阵只使用代码计算的完整数据方差-协方差矩阵，EM本身的代码，和标准的矩阵运算代码。其基本思想是利用EM的收敛速度受缺失信息分数的影响这一事实，找到由于缺失信息而增加的变异性，以添加到完整数据方差-协方差矩阵中。我们称之为补充EM算法的SEM算法。理论和具体的例子加强了SEM算法的结论。
Abstract The expectation maximization (EM) algorithm is a popular, and often remarkably simple, method for maximum likelihood estimation in incomplete-data problems. One criticism of EM in practice is that asymptotic variance–covariance matrices for parameters (e.g., standard errors) are not automatic byproducts, as they are when using some other methods, such as Newton–Raphson. In this article we define and illustrate a procedure that obtains numerically stable asymptotic variance–covariance matrices using only the code for computing the complete-data variance–covariance matrix, the code for EM itself, and code for standard matrix operations. The basic idea is to use the fact that the rate of convergence of EM is governed by the fractions of missing information to find the increased variability due to missing information to add to the complete-data variance–covariance matrix. We call this supplemented EM algorithm the SEM algorithm. Theory and particular examples reinforce the conclusion that the SEM alg...