Title: On the global optimality and asymptotic posterior normality of the generalized extreme value likelihood function
Authors: Likun Zhang - Lawrence Berkeley National Lab (United States) [presenting]
Abstract: The three-parameter generalized extreme value (GEV) distribution arises from classical univariate extreme value theory and is in common use for analyzing the far tail of observed phenomena. Curiously, important asymptotic properties of likelihood-based estimation under this standard model have yet to be established. We first show that the maximum likelihood estimator is global and unique. We then use these results to demonstrate the asymptotic normality of the corresponding posterior distribution under regular priors. These properties are crucial to performing Bayesian optimal derivations such as optimal decision rules and reference prior distributions under the GEV distribution.