A test of sphericity for high-dimensional data and its application for detection of divergently spiked noise
A test of sphericity for high-dimensional data and its application for detection of divergently spiked noise
复制标题
高维数据球形度检验及其在发散尖峰噪声检测中的应用
DOI：
10.1080/07474946.2018.1548850
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发表时间：
2018
期刊：
影响因子：
--
通讯作者：
Nakayama Yugo
中科院分区：
文献类型：
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作者：
Yata Kazuyoshi;Aoshima Makoto;Nakayama Yugo
在本文中，我们考虑了高维协方差矩阵的球度检验。我们通过使用扩展的交叉数据矩阵（ECDM）方法产生检验统计量。我们证明ECDM检验统计量是基于球度测度的无偏估计量。此外，ECDM检验统计量在高维环境下具有一致性和渐近正态性。提出了一种新的基于ECDM检验统计量的检验方法，并从理论上和数值上对其渐近大小和功率进行了评价。我们给出了一个两阶段采样方案，以便测试过程可以确保尺寸和功率的预先指定水平。我们应用测试程序来检测高维统计分析中的发散尖刺噪声。我们通过提出的测试程序分析基因表达数据。
In this article, we consider a test of the sphericity for high-dimensional covariance matrices. We produce a test statistic by using the extended cross-data-matrix (ECDM) methodology. We show that the ECDM test statistic is based on an unbiased estimator of a sphericity measure. In addition, the ECDM test statistic enjoys consistency properties and the asymptotic normality in high-dimensional settings. We propose a new test procedure based on the ECDM test statistic and evaluate its asymptotic size and power theoretically and numerically. We give a two-stage sampling scheme so that the test procedure can ensure a prespecified level both for the size and power. We apply the test procedure to detect divergently spiked noise in high-dimensional statistical analysis. We analyze gene expression data by the proposed test procedure.