Publication
A Note on Second Order Conditions in Extreme Value Theory: Linking General and Heavy Tail Conditions
| Summary: | 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. |
|---|---|
| Main Authors: | Fraga Alves , M. Isabel |
| Other Authors: | Gomes , M. Ivette; de Haan , Laurens; Neves, Cláudia |
| Subject: | extreme value index regular variation semi-parametric estimation |
| Year: | 2007 |
| Country: | Portugal |
| Document type: | article |
| Access type: | unknown |
| Associated institution: | Instituto Nacional de Estatística |
| Language: | English |
| Origin: | REVSTAT-Statistical Journal |
| Summary: | 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. |
|---|