The stochastic approximation method for recursive kernel estimation of the conditional extreme value index

Fatma Ben Khadher , Yousri Slaoui (1)

1 LMA [Poitiers] - Laboratoire de mathématiques et applications [UMR 7348]

In this research paper, our central focus is upon applying the stochastic approximation method to define a class of recursive kernel estimator of the conditional extreme value index. We investigate the properties of the proposed recursive estimator and compare them to those pertaining to Hill's non-recursive kernel estimator. We attempt to demonstrate that using some optimal parameters, the proposed recursive estimator defined by the stochastic approximation algorithm proves to be very competitive to Hill's non-recursive kernel estimator. Finally, the theoretical results are explored through simulation experiments and illustrated using real dataset about Malaria in Senegalese children.

Mots clés: Stochastic approximation algorithm; tail index; extreme value; Pareto distribution

Domaines: Statistiques [stat]

Fatma Ben Khadher, Yousri Slaoui. The stochastic approximation method for recursive kernel estimation of the conditional extreme value index. 2021. ⟨hal-03145485⟩