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Methodology and Computing in Applied Probability

, Volume 10, Issue 4, pp 577–593 | Cite as

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

  • Jürg HüslerEmail author
  • Deyuan Li
Article

Abstract

Let Y i , 1 ≤ in 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 ≤ in} 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.

Keywords

Mean excess function Tail index Linear regression Empirical mean excess process Goodness-of-fit test 

AMS 2000 Subject Classification

62G32 60G70 

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Copyright information

© Springer Science+Business Media, LLC 2007

Authors and Affiliations

  1. 1.Department of Mathematical StatisticsUniversity of BernBernSwitzerland

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