A Note on Second Order Conditions in Extreme Value Theory: Linking General and Heavy Tail Conditions

Authors

  • M. Isabel Fraga Alves University of Lisbon
  • M. Ivette Gomes University of Lisbon
  • Laurens de Haan Erasmus University Rotterdam
  • Cláudia Neves University of Aveiro

DOI:

https://doi.org/10.57805/revstat.v5i3.53

Keywords:

extreme value index, regular variation, semi-parametric estimation

Abstract

Second order conditions ruling the rate of convergence in any first order condition involving regular variation and assuring a unified extreme value limiting distribution function for the sequence of maximum values, linearly normalized, have appeared in several contexts whenever researchers are working either with a general tail, i.e., γ ∈ R, or with heavy tails, with an extreme value index γ > 0. In this paper we shall clarify the link between the second order parameters, say ρ and ρe that have appeared in the two above mentioned set-ups, i.e., for a general tail and for heavy tails, respectively. We illustrate the theory with some examples and, for heavy tails, we provide a link with a third order framework.

Published

2007-12-07

How to Cite

Fraga Alves , M. I., Gomes , M. I., de Haan , L., & Neves, C. (2007). A Note on Second Order Conditions in Extreme Value Theory: Linking General and Heavy Tail Conditions. REVSTAT-Statistical Journal, 5(3), 285–304. https://doi.org/10.57805/revstat.v5i3.53