A quotient-affine Riemannian Gaussian on full-rank correlation matrices has finite moments, exact p=2/Fisher likelihood, and a center-dependent normalizer for p=3 that separates MLE from Fréchet estimation.
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Exact Likelihood and Sampling for Riemannian Gaussian Distributions on Correlation Matrices
A quotient-affine Riemannian Gaussian on full-rank correlation matrices has finite moments, exact p=2/Fisher likelihood, and a center-dependent normalizer for p=3 that separates MLE from Fréchet estimation.