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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A new estimation method for population linear spectral statistics achieves O(n^{ε-1}) convergence for any ε>0 when d/n→c>0 in nonparametric settings, with a CLT for Gaussian data.
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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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Estimation of Population Linear Spectral Statistics by Marchenko--Pastur Inversion
A new estimation method for population linear spectral statistics achieves O(n^{ε-1}) convergence for any ε>0 when d/n→c>0 in nonparametric settings, with a CLT for Gaussian data.