Positive definite estimators of large covariance matrices
Positive definite estimators of large covariance matrices
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DOI：
10.1093/biomet/ass025
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发表时间：
2012-09-01
期刊：
影响因子：
2.7
通讯作者：
Rothman, Adam J.
中科院分区：
文献类型：
--
作者：
Rothman, Adam J.
使用凸优化，我们构造了一个稀疏估计的协方差矩阵是正定的，并在高维设置中表现良好。一个套索型的惩罚是用来鼓励稀疏和对数障碍函数是用来强制正定。一致性和收敛速度界的变量和样本量的数量都建立了分歧。一个有效的计算算法的开发和该方法的优点说明了仿真和语音信号分类的例子。
Using convex optimization, we construct a sparse estimator of the covariance matrix that is positive definite and performs well in high-dimensional settings. A lasso-type penalty is used to encourage sparsity and a logarithmic barrier function is used to enforce positive definiteness. Consistency and convergence rate bounds are established as both the number of variables and sample size diverge. An efficient computational algorithm is developed and the merits of the approach are illustrated with simulations and a speech signal classification example.