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Weak Convergence of the Empirical Mean Excess Process with Application to Estimate the Negative Tail Index

Hüsler, Jürg ; Li, Deyuan

In: Methodology and Computing in Applied Probability, 2008, vol. 10, no. 4, p. 577-593

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    Titre
    • Weak Convergence of the Empirical Mean Excess Process with Application to Estimate the Negative Tail Index
    Auteur
    • Hüsler, Jürg. Department of Mathematical Statistics, University of Bern, Bern, Switzerland
    • Li, Deyuan. Department of Mathematical Statistics, University of Bern, Bern, Switzerland
    Type de document
    • Postprint
    Langue
    • Anglais
    Publié dans
    • Methodology and Computing in Applied Probability, 2008, vol. 10, no. 4, p. 577-593. Springer US; http://www.springer-ny.com
    Autre version électronique
    Identifiant OAI-PMH
    • oai:doc.rero.ch:310690
    Summary
    Let Y i , 1 ≤ i ≤ n be i.i.d. random variables with the generalized Pareto distribution W γ,σ with γ < 0. We define the empirical mean excess process with respect to {Y i , 1 ≤ i ≤ n} as in Eq. 2.1 (see below) and investigate its weak convergence. As an application, two new estimators of the negative tail index γ are constructed based on the linear regression to the empirical mean excess function and their consistency and asymptotic normality are obtained