The Stochastic Approximation Method for Recursive Kernel Estimation of the Conditional Extreme Value Index

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In this research paper, we apply 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 show 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 confirmed through simulation experiments and illustrated using a real dataset about Malaria in Senegalese children.