In extreme value analysis, staring from Smith (1987) [1], the maximum likelihood procedure is applied in estimating the shape parameter of tails--the extreme value index [gamma]. For its theoretical properties, Zhou (2009) [12] proved that the maximum likelihood estimator eventually exists and...

Let X={X(s)}s∈S be an almost sure continuous stochastic process (S compact subset of Rd) in the domain of attraction of some max-stable process, with index function constant over S. We study the tail distribution of ∫SX(s)ds, which turns out to be of Generalized Pareto type with an extra...

The paper is about the asymptotic properties of the maximum likelihood estimator for the extreme value index. Under the second order condition, Drees et al. [H. Drees, A. Ferreira, L. de Haan, On maximum likelihood estimation of the extreme value index, Ann. Appl. Probab. 14 (2004) 1179-1201]...