Inference for High-dimensional Differential Correlation Matrices.
Inference for High-dimensional Differential Correlation Matrices.
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DOI：
10.1016/j.jmva.2015.08.019
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发表时间：
2016-01-01
影响因子：
1.6
通讯作者：
Zhang A
中科院分区：
文献类型：
--
作者：
Cai TT;Zhang A
受基因组学中差异共表达分析的启发，本文考虑了高维差异相关矩阵的估计和检验。介绍了一种自适应阈值处理方法，并给出了理论保证。建立了极大极小收敛速率，并证明了该估计器在具有近似稀疏差异的成对相关矩阵集合上具有自适应速率最优。仿真结果表明，该方法明显优于其他两种基于单独估计单个相关矩阵的自然方法。该程序还通过对乳腺癌数据集的分析来说明，该数据集在基因共表达水平上提供了证据，表明几个基因（其中一个子集已被先前验证）与乳腺癌相关。对微分相关矩阵的假设检验也被考虑。介绍了一个特别适合针对稀疏替代方案进行测试的测试。此外，还讨论了其他相关问题，包括单个稀疏相关矩阵的估计、微分协方差矩阵的估计和微分互相关矩阵的估计。
Motivated by differential co-expression analysis in genomics, we consider in this paper estimation and testing of high-dimensional differential correlation matrices. An adaptive thresholding procedure is introduced and theoretical guarantees are given. Minimax rate of convergence is established and the proposed estimator is shown to be adaptively rate-optimal over collections of paired correlation matrices with approximately sparse differences. Simulation results show that the procedure significantly outperforms two other natural methods that are based on separate estimation of the individual correlation matrices. The procedure is also illustrated through an analysis of a breast cancer dataset, which provides evidence at the gene co-expression level that several genes, of which a subset has been previously verified, are associated with the breast cancer. Hypothesis testing on the differential correlation matrices is also considered. A test, which is particularly well suited for testing against sparse alternatives, is introduced. In addition, other related problems, including estimation of a single sparse correlation matrix, estimation of the differential covariance matrices, and estimation of the differential cross-correlation matrices, are also discussed.