Tests for covariance matrices in high dimension with less sample size
Tests for covariance matrices in high dimension with less sample size
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DOI：
10.1016/j.jmva.2014.06.003
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发表时间：
2014-09
期刊：
影响因子：
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通讯作者：
M. Srivastava;H. Yanagihara;T. Kubokawa
中科院分区：
文献类型：
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作者：
M. Srivastava;H. Yanagihara;T. Kubokawa
在这篇文章中，我们提出了检验高维协方差矩阵的较少的观察比一般类的分布正定协方差矩阵的维数。在单样本情况下，提出了球度检验和协方差矩阵是单位矩阵的假设检验，通过在一般模型下提供tr的无偏估计量，其计算时间不超过文献中的正态模型。在两个样本的情况下，测试的两个协方差矩阵的平等。在样本容量N= O（p δ），1/2< δ< 1的假设下，导出了单样本情况下所提出的检验的渐近分布，其中p是随机向量的维数，O（p δ）表示当N和p趋于无穷大时N/p趋于零.在两个样本的情况下也作了类似的假设。
In this article, we propose tests for covariance matrices of high dimension with fewer observations than the dimension for a general class of distributions with positive definite covariance matrices. In the one-sample case, tests are proposed for sphericity and for testing the hypothesis that the covariance matrix Σ is an identity matrix, by providing an unbiased estimator of tr [Σ 2] under the general model which requires no more computing time than the one available in the literature for a normal model. In the two-sample case, tests for the equality of two covariance matrices are given. The asymptotic distributions of proposed tests in the one-sample case are derived under the assumption that the sample size N= O (p δ), 1/2< δ< 1, where p is the dimension of the random vector, and O (p δ) means that N/p goes to zero as N and p go to infinity. Similar assumptions are made in the two-sample case.