On sparsity scales and covariance matrix transformations
On sparsity scales and covariance matrix transformations
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DOI：
10.1093/biomet/asz014
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发表时间：
2019-09
期刊：
影响因子：
2.7
通讯作者：
H. Battey
中科院分区：
文献类型：
--
作者：
H. Battey
当矩阵维数大于样本容量时，我们在任何给定的或估计的稀疏尺度上建立了协方差和浓度矩阵估计的理论。当这些矩阵是讨厌的参数时，非标准稀疏尺度是合理的，不同于兴趣参数，它应该总是有一个直接的主题解释。矩阵的对数和逆尺度的特殊情况下进行了研究，与推论的约束优化为基础的方法是不必要的估计稀疏浓度矩阵。通过模拟表明，对于大型非结构化协方差矩阵，估计对数变换协方差矩阵的稀疏近似并将结论转换回感兴趣的尺度可能具有明显的优势。
We develop a theory of covariance and concentration matrix estimation on any given or estimated sparsity scale when the matrix dimension is larger than the sample size. Nonstandard sparsity scales are justified when such matrices are nuisance parameters, distinct from interest parameters, which should always have a direct subject-matter interpretation. The matrix logarithmic and inverse scales are studied as special cases, with the corollary that a constrained optimization-based approach is unnecessary for estimating a sparse concentration matrix. It is shown through simulations that for large unstructured covariance matrices, there can be appreciable advantages to estimating a sparse approximation to the log-transformed covariance matrix and converting the conclusions back to the scale of interest.