Inferences on Generalized Qi’s Estimators

Source abstract

Assuming that all observations are available for analysis, we consider block-type estimators, which are presented as some function of generalized Qi statistics, for a positive extreme value index. Weak consistency and asymptotic normality of the estimators under consideration are proved. Also, we compare theoretically the considered estimators with corresponding peaks-over-threshold-type estimators, i.e., which are the same function of generalized Hill statistics. We prove that these estimators do not dominate each other. The practical validation of asymptotic comparison results for finite samples is done by means of Monte-Carlo simulation for several heavy-tailed models.