Title: Empirical Bayes analysis of maxima
Authors: Stefano Rizzelli - Catholic University - Milan (Italy) [presenting]
Simone Padoan - Bocconi University (Italy)
Abstract: Predicting future observations is the central goal of several statistical applications concerning extreme value data. Under mild assumptions, extreme-value theory justifies modelling linearly normalized sample maxima by max-stable distributions. The Bayesian paradigm offers a direct approach to forecasting and uncertainty quantification. 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. We propose an empirical Bayes approach that suitably addresses this point via data-dependent priors. We illustrate the resulting asymptotic posterior concentration properties and pinpoint their implications for the estimation and prediction of future observations.