MM Algorithms for Variance Components Models
MM Algorithms for Variance Components Models
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DOI：
10.1080/10618600.2018.1529601
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发表时间：
2019-04-03
影响因子：
2.4
通讯作者：
Lange, Kenneth
中科院分区：
文献类型：
--
作者：
Zhou, Hua;Hu, Liuyi;Lange, Kenneth
方差分量估计和混合模型分析是统计学中的中心主题，在许多科学学科中都有应用。尽管一代又一代的统计学家和数值分析师尽了最大的努力，方差分量模型的最大似然估计（MLE）和限制性MLE仍然具有数值挑战性。基于最小化-最大化（MM）原理，提出了一种新的方差分量估计迭代算法。我们的MM算法是平凡的实现和竞争力的大数据问题。该算法很容易扩展到更复杂的问题，如线性混合模型，多变量响应模型可能与缺失数据，最大后验估计，惩罚估计。我们建立了MM算法的Karush-Kuhn-Tucker点的全局收敛性，并从数值和理论上证明了，当方差分量的数量大于2且所有协方差矩阵都是正定的时，它比经典EM算法收敛得更快。可以在网上找到。
Variance components estimation and mixed model analysis are central themes in statistics with applications in numerous scientific disciplines. Despite the best efforts of generations of statisticians and numerical analysts, maximum likelihood estimation (MLE) and restricted MLE of variance component models remain numerically challenging. Building on the minorization-maximization (MM) principle, this article presents a novel iterative algorithm for variance components estimation. Our MM algorithm is trivial to implement and competitive on large data problems. The algorithm readily extends to more complicated problems such as linear mixed models, multivariate response models possibly with missing data, maximum a posteriori estimation, and penalized estimation. We establish the global convergence of the MM algorithm to a Karush-Kuhn-Tucker point and demonstrate, both numerically and theoretically, that it converges faster than the classical EM algorithm when the number of variance components is greater than two and all covariance matrices are positive definite. for this article are available online.