Il Dipartimento di Statistica e Metodi Quantitativi dell’Università di Milano Bicocca (Via Bicocca degli Arcimboldi, 8 MILANO) invita al seguente seminario. Venerdì 19 settembre, alle ore 11.30, nell'aula Consiglio della Scuola di Economia e Statistica 4° piano, Edificio U7, il Prof. Abdelhakim Necir terrà il seguente seminario:

A Kaplan-Meier process for a heavy-tail distribution toward

the tail index estimation under random censoring

Abdelhakim Necir

Laboratory of Applied Mathematics, University Mohamed Khider of Biskra, Algeria

Abstract:

In the case of complete data, weak approximations to tail empirical processes for heavy-tailed distributions have been established by many authors. In this paper, we consider the random censoring setting through a tail Kaplan-Meier process and define a new estimator of the extreme value index. Under mild conditions, we establish the consistency and asymptotic normality of the proposed estimator and, through an extensive simulation study, we investigate its performance and compare it to the adapted Hill estimator introduced by Einmahl et al. (2008). Our result will be of great interest to derive the limit distributions of many statistics based on extreme values for randomly censored data such as the estimators of tail indices, actuarial risk measures and goodness-of-fit functionals.