Bounded overestimation of the number of factors in PCA preserves √T-valid inference and consistent factor-space recovery under a random-matrix local law.
The Annals of Statistics , volume=
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Proves sharp operator-norm concentration and expectation bounds for sample cross-covariances of sub-Gaussian and Gaussian vectors, governed by effective ranks of the marginal covariances.
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Fixed-order PCA: Theory for Overestimated Factor Models
Bounded overestimation of the number of factors in PCA preserves √T-valid inference and consistent factor-space recovery under a random-matrix local law.
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Concentration Inequalities for Sample Cross-Covariances
Proves sharp operator-norm concentration and expectation bounds for sample cross-covariances of sub-Gaussian and Gaussian vectors, governed by effective ranks of the marginal covariances.