2025/10/20 by Enkelejd Hashorva, Hashorva, Enkelejd
Mathematics · #Random Matrices and Applications #Markov Chains and Monte Carlo Methods #Statistical Methods and Inference
paper · pdf · doi:10.48550/arxiv.2510.18094
We derive explicit comparison bounds for multivariate max-stable distributions with unit-α-Fréchet margins. For the Kolmogorov distance, the bounds are expressed through Wasserstein distances between powered de Haan representers, total variation distances between angular measures, and discrepancies of the Ψ-functions in the inf--argmax decomposition. On the positive ℓα-sphere, the coefficient multiplying the setwise angular total-variation distance contains no explicit dimension factor for the unnormalised angular measures used here. Separately, for 1≤ p<α, a synchronous de Haan--LePage coupling bounds the p-Wasserstein distance between the max-stable laws by an α-Wasserstein transport cost between their unpowered de Haan representers. We also compare laws with a common extreme-value copula and different Fréchet indices, obtaining an exact ℓ1-Wasserstein formula when p=1, and discuss applications to Archimax and clustered Archimax copulas and to Brown--Resnick/Hüsler--Reiss models.