SPARSE ESTIMATION OF LARGE COVARIANCE MATRICES VIA A NESTED LASSO PENALTY
SPARSE ESTIMATION OF LARGE COVARIANCE MATRICES VIA A NESTED LASSO PENALTY
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DOI：
10.1214/07-aoas139
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发表时间：
2008-03-01
影响因子：
1.8
通讯作者：
Zhu, Ji
中科院分区：
文献类型：
--
作者：
Levina, Elizaveta;Rothman, Adam;Zhu, Ji
本文提出了一种新的协方差估计的大协方差矩阵时，变量有如果自然序。利用Cholesky分解的逆，我们施加如果手的结构上的Cholesky因子，并选择带宽自适应的Cholesky因子的每一行，使用一种新的惩罚，我们称之为嵌套Lasso。这种结构比常规的条带化更灵活，但与应用于Cholesky因子的条目的常规Lasso不同，它会导致协方差矩阵的逆的稀疏估计量。矩阵提出了一种求解最优化问题的迭代算法。估计量进行了比较，一些其他的协方差估计，并显示最好的，无论是在模拟和一个真实的数据的例子。仿真结果表明，估计优于其竞争对手的利润率往往增加与维数。
The paper proposes a new covariance estimator for large covariance matrices when the variables have if natural ordering. Using the Cholesky decomposition of the inverse, we impose if handed structure on the Cholesky factor, and select the bandwidth adaptively for each row of the Cholesky factor, using a novel penalty we call nested Lasso. This structure has more flexibility than regular banding, but, unlike regular Lasso applied to the entries of the Cholesky factor, results in a sparse estimator for the inverse of the covariance matrix. matrix. An iterative algorithm for solving the optimization problem is developed. The estimator is compared to a number of other covariance estimators and is shown to de best, both in simulations and on a real data example. Simulations show that the margin by which the estimator outperforms its competitors tends to increase with dimension.