Asymptotics of eigenstructure of sample correlation matrices for high-dimensional spiked models.
Asymptotics of eigenstructure of sample correlation matrices for high-dimensional spiked models.
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DOI：
10.5705/ss.202019.0052
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发表时间：
2021-04
影响因子：
1.4
通讯作者：
Yang J
中科院分区：
文献类型：
--
作者：
Morales-Jimenez D;Johnstone IM;McKay MR;Yang J
Sample correlation matrices are widely used, but for high-dimensional data little is known about their spectral properties beyond “null models”, which assume the data have independent coordinates. In the class of spiked models, we apply random matrix theory to derive asymptotic first-order and distributional results for both leading eigenvalues and eigenvectors of sample correlation matrices, assuming a high-dimensional regime in which the ratio p/n, of number of variables p to sample size n, converges to a positive constant. While the first-order spectral properties of sample correlation matrices match those of sample covariance matrices, their asymptotic distributions can differ significantly. Indeed, the correlation-based fluctuations of both sample eigenvalues and eigenvectors are often remarkably smaller than those of their sample covariance counterparts.
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