Empirical Bayesian analysis of componentwise maxima in multivariate samples

Statistical theory and methods for the analysis of maxima, computed componentwise in a multivariate sample, has been an active research area in the last decade. Under mild assumptions, extreme-value theory justifies modelling random vectors of linearly normalized sample maxima by multivariate max-stable distributions. Various proposals for Bayesian inferential procedures have been formulated in recent years, though they typically disregard the asymptotic bias inherent in the use of max-stable models, incorporating no information on norming sequences in prior specifications for scale and location parameters. The semiparametric empirical Bayesian approach in Padoan and Rizzelli (2022) suitably addresses this point via data-dependent priors. In this contribution we review its consistency properties.