Covariance reducing models: An alternative to spectral modelling of covariance matrices

R. Dennis Cook, Liliana Forzani

Research output: Contribution to journalArticlepeer-review

13 Scopus citations


We introduce covariance reducing models for studying the sample covariance matrices of a random vector observed in different populations. The models are based on reducing the sample covariance matrices to an informational core that is sufficient to characterize the variance heterogeneity among the populations. They possess useful equivariance properties and provide a clear alternative to spectral models for covariance matrices.

Original languageEnglish (US)
Pages (from-to)799-812
Number of pages14
Issue number4
StatePublished - Dec 2008

Bibliographical note

Funding Information:
Research for this article was supported in part by a grant from the U.S. National Science Foundation, and by Fellowships from the Isaac Newton Institute for Mathematical Sciences, Cambridge, U.K. The authors are grateful to Patrick Phillips for providing the covariance matrices for the garter snake illustration, and to the referees for their helpful comments.


  • Central subspace
  • Dimension reduction
  • Envelopes
  • Grassmann manifolds
  • Reducing subspaces


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