Uniqueness and global optimality of the maximum likelihood estimator for the generalized extreme value distribution
广义极值分布最大似然估计的唯一性与全局最优性
Summary The three-parameter generalized extreme value distribution arises from classical univariate extreme value theory, and is in common use for analysing the far tail of observed phenomena, yet important asymptotic properties of likelihood-based estimation under this standard model have not been established. In this paper we prove that the maximum likelihood estimator is global and unique. An interesting secondary result entails the uniform consistency of a class of limit…