Zhang, X., Blanchet, J., Marzouk, Y., Nguyen, V. A., & Wang, S. (2023). Wasserstein-based Minimax Estimation of Dependence in Multivariate Regularly Varying Extremes. ArXiv. /abs/2312.09862

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Abstract

We study minimax risk bounds for estimators of the spectral measure in multivariate linear factor models, where observations are linear combinations of regularly varying latent factors. Non-asymptotic convergence rates are derived for the multivariate Peak-over-Threshold estimator in terms of the -th order Wasserstein distance, and information-theoretic lower bounds for the minimax risks are established. The convergence rate of the estimator is shown to be minimax optimal under a class of Pareto-type models analogous to the standard class used in the setting of one-dimensional observations known as the Hall-Welsh class. When the estimator is minimax inefficient, a novel two-step estimator is introduced and demonstrated to attain the minimax lower bound. Our analysis bridges the gaps in understanding trade-offs between estimation bias and variance in multivariate extreme value theory.

Authors
Xuhui Zhang, Jose Blanchet, Youssef Marzouk, Viet Anh Nguyen, Sven Wang
Publication date
2023/12/15
Journal
arXiv preprint arXiv:2312.09862