Two-Sample Covariance Matrix Testing and Support Recovery in High-Dimensional and Sparse Settings
高维稀疏环境中的两样本协方差矩阵检验与支持集恢复AI 解读 ↓
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高维稀疏环境中的两样本协方差矩阵检验与支持集恢复
- 研究问题
- 如何在高维环境中检验两个协方差矩阵是否相同，并在发现差异后进一步定位相关支持集及逐行差异，以服务基因筛选？
- 方法与思路
- 作者提出协方差相等检验，研究零假设极限分布与功效，并另行构造支持集恢复和逐行检验程序，配合模拟及癌症数据应用。
- 材料陈述的贡献
- 摘要称，新检验具有某些最优性，对稀疏备择尤其有力，模拟中的尺寸与功效优于比较方法；另提供差异定位程序及性质分析。
- 阅读关注点
- 应核对缺失符号所对应的检验对象、稀疏备择定义、最优性的具体标准，以及支持集恢复条件、逐行检验的多重比较处理。
- 阅读边界
- 仅依据 OpenAlex 摘要，不能推断刊本变化。原假设及支持集对象的数学符号缺失，需查阅原文，不能重构公式或判断最优性范围。
原文摘要
In the high-dimensional setting, this article considers three interrelated problems: (a) testing the equality of two covariance matrices and ; (b) recovering the support of ; and (c) testing the equality of and row by row. We propose a new test for testing the hypothesis H 0: and investigate its theoretical and numerical properties. The limiting null distribution of the test statistic is derived and the power of the test is studied. The test is shown to enjoy certain optimality and to be especially powerful against sparse alternatives. The simulation results show that the test significantly outperforms the existing methods both in terms of size and power. Analysis of a prostate cancer dataset is carried out to demonstrate the application of the testing procedures. When the null hypothesis of equal covariance matrices is rejected, it is often of significant interest to further investigate how they differ from each other. Motivated by applications in genomics, we also consider recovering the support of and testing the equality of the two covariance matrices row by row. New procedures are introduced and their properties are studied. Applications to gene selection are also discussed. Supplementary materials for this article are available online.