Maximum likelihood and restricted maximum likelihood estimation for a class of Gaussian Markov random fields
Maximum likelihood and restricted maximum likelihood estimation for a class of Gaussian Markov random fields
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DOI：
10.1007/s00184-009-0295-7
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发表时间：
2011-09
期刊：
影响因子：
0.7
通讯作者：
Victor De Oliveira;Marco A. R. Ferreira
中科院分区：
文献类型：
--
作者：
Victor De Oliveira;Marco A. R. Ferreira
本文描述了一个高斯马尔可夫随机场模型，其中包括几个以前提出的模型，并研究了其最大似然（ML）和限制最大似然（REML）估计在特殊情况下的性质。具体来说，对于模型的回归和精度矩阵之间存在特定关系的模型，我们提供了协方差参数的ML和REML估计的存在性和唯一性的充分条件，并提供了一种简单的方法来计算它们。结果表明，ML估计总是存在的，而REML估计可能不存在的正概率。数值比较表明，对于这个模型ML估计的协方差参数，总体而言，更好的频率属性比REML估计。
This work describes a Gaussian Markov random field model that includes several previously proposed models, and studies properties of its maximum likelihood (ML) and restricted maximum likelihood (REML) estimators in a special case. Specifically, for models where a particular relation holds between the regression and precision matrices of the model, we provide sufficient conditions for existence and uniqueness of ML and REML estimators of the covariance parameters, and provide a straightforward way to compute them. It is found that the ML estimator always exists while the REML estimator may not exist with positive probability. A numerical comparison suggests that for this model ML estimators of covariance parameters have, overall, better frequentist properties than REML estimators.