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A useful variant of the Davis–Kahan theorem for statisticians
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Yu, Yi, Wang, T. and Samworth, R. J. (2015) A useful variant of the Davis–Kahan theorem for statisticians. Biometrika, 102 (2). pp. 315-323. doi:10.1093/biomet/asv008 ISSN 0006-3444.
An open access version can be found in:
Official URL: http://dx.doi.org/10.1093/biomet/asv008
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.
| Item Type: | Journal Article | ||||||
|---|---|---|---|---|---|---|---|
| Divisions: | Faculty of Science, Engineering and Medicine > Science > Statistics | ||||||
| Journal or Publication Title: | Biometrika | ||||||
| Publisher: | Biometrika Trust | ||||||
| ISSN: | 0006-3444 | ||||||
| Official Date: | June 2015 | ||||||
| Dates: |
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| Volume: | 102 | ||||||
| Number: | 2 | ||||||
| Page Range: | pp. 315-323 | ||||||
| DOI: | 10.1093/biomet/asv008 | ||||||
| Status: | Peer Reviewed | ||||||
| Publication Status: | Published | ||||||
| Access rights to Published version: | Restricted or Subscription Access | ||||||
| Related URLs: | |||||||
| Open Access Version: |
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