A useful variant of the Davis-Kahan theorem for statisticians

• 成果类型: Article
• 署名作者: Yu, Y.; Wang, T.; Samworth, R. J.
• 署名单位: University of Cambridge
• 刊物名称: BIOMETRIKA
• ISSN/ISSBN: 0006-3444
• DOI: 10.1093/biomet/asv008
• 发表日期: 2015
• 页码: 315323
• 关键词: optimal rates; matrix

摘要

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.