On the Maximum Likelihood Estimation of Extreme Value Index Based on k-Record Values

Abstract EN

In this paper, we study the existence and consistency of the maximum likelihood estimator of the extreme value index based on k-record values.

Following the method used by Drees et al.

(2004) and Zhou (2009), we prove that the likelihood equations, in terms of k-record values, eventually admit a strongly consistent solution without any restriction on the extreme value index, which is not the case in the aforementioned studies.