Yu, Y;
Wang, T;
Samworth, RJ;
(2015)
A useful variant of the Davis-Kahan theorem for statisticians.
Biometrika
, 102
(2)
pp. 315-323.
10.1093/biomet/asv008.
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Abstract
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.
| Type: | Article |
|---|---|
| Title: | A useful variant of the Davis-Kahan theorem for statisticians |
| Open access status: | An open access version is available from UCL Discovery |
| DOI: | 10.1093/biomet/asv008 |
| Publisher version: | https://doi.org/10.1093/biomet/asv008 |
| Language: | English |
| Additional information: | This version is the author accepted manuscript. For information on re-use, please refer to the publisher’s terms and conditions. |
| Keywords: | Davis–Kahan theorem; Eigendecomposition; Matrix perturbation; Singular value decomposition |
| UCL classification: | UCL UCL > Provost and Vice Provost Offices > UCL BEAMS UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences > Dept of Statistical Science |
| URI: | https://discovery.ucl.ac.uk/id/eprint/10055409 |
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