Asymptotics of eigenstructure of sample correlation matrices for high-dimensional spiked models

David Morales-Jimenez, Iain M. Johnstone, Matthew R. McKay, Jeha Yang

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31 Citations (Scopus)
56 Downloads (Pure)


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 , of number of variables to sample size , 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.
Original languageEnglish
Pages (from-to)571-601
Number of pages31
JournalStatistica Sinica
Issue number2
Publication statusPublished - Apr 2021

Bibliographical note

Funding Information:
This work was supported, in part, by NIH R01 EB001988 and RO1 GM134483 (IMJ, JY), the Hong Kong RGC General Research Fund 16202918 (MRM, DMJ), and a Samsung Scholarship (JY).

Publisher Copyright:
© 2021 Institute of Statistical Science. All rights reserved.

Copyright 2021 Elsevier B.V., All rights reserved.


  • Sample correlation
  • eigenstructure
  • spiked models

ASJC Scopus subject areas

  • Statistics and Probability
  • Statistics, Probability and Uncertainty


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