FLEXIBLE COVARIANCE ESTIMATION IN GRAPHICAL GAUSSIAN MODELS
FLEXIBLE COVARIANCE ESTIMATION IN GRAPHICAL GAUSSIAN MODELS
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DOI：
10.1214/08-aos619
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发表时间：
2008-12-01
影响因子：
4.5
通讯作者：
Carvalho, Carlos M.
中科院分区：
文献类型：
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作者：
Rajaratnam, Bala;Massam, Helene;Carvalho, Carlos M.
本文提出了图高斯模型关于可分解图G的马氏协方差阵的一类Bayes估计。工作与W-PG家庭定义的Letac和Massam [安。35（2007）1278-1323]中，我们导出了熵和平方误差损失下的贝叶斯估计的封闭形式表达式。W-PG家族包括超逆Wishart的经典逆，但具有更多的形状参数，从而允许在差分收缩协方差矩阵的各个部分时的灵活性。此外，使用这个家庭避免求助于MCMC，往往是不可行的高维问题。我们通过一系列数值例子来说明我们的估计器的性能，在这些例子中，我们探索了频率论风险属性和高维协方差结构估计中图形的功效。
In this paper, we propose a class of Bayes estimators for the covariance matrix of graphical Gaussian models Markov with respect to a decomposable graph G. Working with the W-PG family defined by Letac and Massam [Ann. Statist. 35 (2007) 1278-1323] we derive closed-form expressions for Bayes estimators under the entropy and squared-error losses. The W-PG family includes the classical inverse of the hyper inverse Wishart but has many more shape parameters, thus allowing for flexibility in differentially shrinking various parts of the covariance matrix. Moreover, using this family avoids recourse to MCMC, often infeasible in high-dimensional problems. We illustrate the performance of our estimators through a collection of numerical examples where we explore frequentist risk properties and the efficacy of graphs in the estimation of high-dimensional covariance structures.