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

R. Dennis Cook; Liliana Forzani

doi:10.1093/biomet/asn052

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

R. Dennis Cook, Liliana Forzani

Statistics (Twin Cities)

Research output: Contribution to journal › Article › peer-review

15 Scopus citations

Abstract

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 language	English (US)
Pages (from-to)	799-812
Number of pages	14
Journal	Biometrika
Volume	95
Issue number	4
DOIs	https://doi.org/10.1093/biomet/asn052
State	Published - 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.

Keywords

Central subspace
Dimension reduction
Envelopes
Grassmann manifolds
Reducing subspaces

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abstract = "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.",

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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.",

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KW - Envelopes

KW - Grassmann manifolds

KW - Reducing subspaces

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

Abstract

Bibliographical note

Keywords

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