Derives dimension-independent finite-sample operator-norm bounds for selected covariance estimation in classical shadows via matrix Bernstein and perturbation theory.
A useful variant of the Davis--Kahan theorem for statisticians
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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 relevant 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 improving the bounds in some cases. We also provide 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.
years
2026 2verdicts
UNVERDICTED 2representative citing papers
Spectral graph analysis of the Hilbert-space connectivity graph detects exact fragmentation and nearly fragmented sectors with slow leakage in the t-J model and Hubbard chain.
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Finite-Sample Selected Covariance Spectra in Classical Shadows
Derives dimension-independent finite-sample operator-norm bounds for selected covariance estimation in classical shadows via matrix Bernstein and perturbation theory.
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Graph-Theoretic Detection of Hilbert Space Fragmentation
Spectral graph analysis of the Hilbert-space connectivity graph detects exact fragmentation and nearly fragmented sectors with slow leakage in the t-J model and Hubbard chain.