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arXiv 1408.5907stat.MEmath.STstat.TH
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高维差分相关矩阵的推断

Inference for High-dimensional Differential Correlation Matrices

T. Tony Cai, Anru Zhang

摘要:

受基因组学中差异共表达分析的启发,本文考虑高维差异相关矩阵的估计和检验。一个自适应阈值的过程中引入和理论保证。极小极大收敛速度的建立和建议的估计是自适应率最优的集合的成对相关矩阵与近似稀疏的差异。仿真结果表明,该过程显着优于其他两个自然的方法,是基于单独的相关矩阵的估计。该程序还说明了通过分析的乳腺癌数据集,它提供了证据,在基因共表达水平的几个基因,其中的一个子集已被事先验证,与乳腺癌。还考虑了对差分相关矩阵的假设检验。一个测试,这是特别适合于测试对稀疏的替代品,介绍。此外,还讨论了其它相关问题,包括单个稀疏相关矩阵的估计、差分协方差阵的估计和差分互相关矩阵的估计。

英文摘要:

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.

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

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