Asymptotic distributions of functions of the eigenvalues of some random matrices for nonnormal populations

Fang & Krishnaiah (1982) — functions of eigenvalues, nonnormal populations

Result

limit laws of smooth functions of the eigenvalues of the standard covariance/MANOVA/canonical-correlation random matrices under nonnormal sampling (fourth-cumulant covariance).

Use

the closest general theorem to "$\sqrt n(\hat\eta_D-\eta_D)$ is normal", and the one that covers repeated $\rho_i$ — the abstract states the results are for population eigenvalues with multiplicities, which the determinant route of O7.2 also tolerates. Cited for the method in RETENTION-PLUGIN-CLT-FROZEN-VECTOR.

Verification

abstract read verbatim (primary text via RePEc and ScienceDirect metadata, 6 Sep 2026); theorem numbering and the covariance formula unread.