Journal
BIOMETRIKA
Volume 102, Issue 2, Pages 315-323Publisher
OXFORD UNIV PRESS
DOI: 10.1093/biomet/asv008
Keywords
Davis-Kahan theorem; Eigendecomposition; Matrix perturbation; Singular value decomposition
Funding
- Engineering and Physical Sciences Research Council Early Career Fellowship
- Benefactors' scholarship from St John's College, Cambridge
- Engineering and Physical Sciences Research Council [EP/J017213/1] Funding Source: researchfish
- EPSRC [EP/J017213/1] Funding Source: UKRI
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The Davis-Kahan theorem is used in the analysis of many statistical procedures to bound the distance between subspaces spanned by population eigenvectors and their sample versions. It relies on an eigenvalue separation condition between certain population and sample eigenvalues. We present a variant of this result that depends only on a population eigenvalue separation condition, making it more natural and convenient for direct application in statistical contexts, and provide an improvement in many cases to the usual bound in the statistical literature. We also give an extension to situations where the matrices under study may be asymmetric or even non-square, and where interest is in the distance between subspaces spanned by corresponding singular vectors.
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