Resolvents of the sample covariances in the separable mixture model approximate deterministic matrices defined via solutions to a dual system of equations, without simultaneous diagonalizability assumptions.
On the principal components of sample covariance matrices
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Proves approximate Gaussianity of debiased linear forms of eigenvectors in matrix denoising and spiked PCA models under Gaussian noise, then constructs bias/variance estimators yielding minimax-optimal confidence intervals without sample splitting.
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Spectral approximation for the separable covariance mixture model
Resolvents of the sample covariances in the separable mixture model approximate deterministic matrices defined via solutions to a dual system of equations, without simultaneous diagonalizability assumptions.
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Statistical Inference for Linear Functions of Eigenvectors with Small Eigengaps
Proves approximate Gaussianity of debiased linear forms of eigenvectors in matrix denoising and spiked PCA models under Gaussian noise, then constructs bias/variance estimators yielding minimax-optimal confidence intervals without sample splitting.