2023/12/15 by Xuhui Zhang, Zhang, Xuhui, José Blanchet +7 · 1 citation
Decision Sciences · Mathematics · #FOS: Computer and information sciences #FOS: Mathematics #Methodology (stat.ME) #Probabilistic and Robust Engineering Design #Statistical Methods and Inference #Statistics Theory (math.ST)
paper · pdf · doi:10.48550/arxiv.2312.09862
openalex publication_date 2023/12/15 · openalex created_date 2023/12/19 · openalex updated_date 2026/07/28
We present the first 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 p-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.