Uniqueness and global optimality of the maximum likelihood estimator for the generalized extreme value distribution
证明了广义极值分布下最大似然估计的全局唯一性，并得到形状参数邻域内极限关系的一致收敛性，对极值分析和风险建模有重要价值。
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 relations in a tight neighbourhood of the true shape parameter.