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Biometrika Advance Access published online on November 11, 2008
Biometrika, doi:10.1093/biomet/asn052
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© 2008 Biometrika Trust

Article

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

R. Dennis Cook

School of Statistics, University of Minnesota, Minneapolis, Minnesota 55455, U.S.A. dennis{at}stat.umn.edu

Liliana Forzani

Facultad de Ingeniería Química, Universidad Nacional del Litoral and Instituto Matemática Aplicada Litoral, CONICET, Santa Fe, Argentina liliana.forzani{at}gmail.com

Received for publication 1 December 2007. Revision received 1 April 2008.
  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.

Key Words: Central subspace • Dimension reduction • Envelopes • Grassmann manifolds • Reducing subspaces


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