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.
Bibliographical noteFunding 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
- Grassmann manifolds
- Reducing subspaces