Afrika Statistika

A Lynden-Bell integral estimator for the tail index of right-truncated data with a random threshold

Nawel Haouas,, Abdelhakim Necir, Djamel Meraghni, and Brahim Brahimi

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Abstract

By means of a Lynden-Bell integral with deterministic threshold, Worms and Worms [A Lynden-Bell integral estimator for extremes of randomly truncated data. Statist. Probab. Lett. 2016; 109: 106-117] recently introduced an asymptotically normal estimator of the tail index for randomly right-truncated Pareto-type data. In this context, we consider the random threshold case to derive a Hill-type estimator and establish its consistency and asymptotic normality. A simulation study is carried out to evaluate the finite sample behavior of the proposed estimator.

Résumé

Par l'intégrale de Lynden-Bell avec un seuil déterministe, Worms et Worms [A Lynden-Bell integral estimator for extremes of randomly truncated data. Statist. Probab. Lett. 2016; 109: 106-117] a récemment introduit un estimateur asymptotiquement normal de l'indice de queue pour les données de type Pareto tronquées à droit. Dans ce contexte, nous considérons le cas du seuil aléatoire pour obtenir un estimateur de type Hill et établir sa consistance et sa normalité asymptotique. Une étude de simulation est réalisée pour évaluer le comportement de l'estimateur proposé.

Article information

Source
Afr. Stat., Volume 12, Number 1 (2017), 1159-1170.

Dates
Received: 2 December 2016
Accepted: 3 March 2017
First available in Project Euclid: 22 April 2017

Permanent link to this document
https://projecteuclid.org/euclid.as/1492826419

Digital Object Identifier
doi:10.16929/as/2017.1159.97

Mathematical Reviews number (MathSciNet)
MR3638976

Zentralblatt MATH identifier
1366.62101

Subjects
Primary: 60F17: Functional limit theorems; invariance principles 62G30: Order statistics; empirical distribution functions 62G32: Statistics of extreme values; tail inference 62P05: Applications to actuarial sciences and financial mathematics

Keywords
Extreme value index Heavy-tails Lynden-Bell estimator Random truncation

Citation

Haouas,, Nawel; Necir, Abdelhakim; Meraghni, Djamel; Brahimi, Brahim. A Lynden-Bell integral estimator for the tail index of right-truncated data with a random threshold. Afr. Stat. 12 (2017), no. 1, 1159--1170. doi:10.16929/as/2017.1159.97. https://projecteuclid.org/euclid.as/1492826419


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