For multi-index models, the eigenvalues, eigenvector overlaps, and optimal preprocessing of spectral estimators are characterized exactly in the proportional asymptotics.
Phase transition of the largest eigenvalue for nonnull complex sample covariance matrices
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Spectral Estimators for Multi-Index Models: Precise Asymptotics and Optimal Weak Recovery
For multi-index models, the eigenvalues, eigenvector overlaps, and optimal preprocessing of spectral estimators are characterized exactly in the proportional asymptotics.