The generalization of several classical estimators for a positive extreme value index
Pub. online: 19 March 2026
Type: Research Article
Open Access
Open Access
Received
6 September 2025
6 September 2025
Revised
9 February 2026
9 February 2026
Accepted
26 February 2026
26 February 2026
Published
19 March 2026
19 March 2026
Abstract
In this paper, we introduce a family of semi-parametric estimators for the positive extreme value index γ, parameterized in two tuning parameters. The asymptotic normality of the introduced estimators is proved. It is shown that the partial case of newly introduced estimators (a subfamily with one tuning parameter) has quite good asymptotic properties and dominates several previously introduced estimators. Small Monte-Carlo simulations are included. Also, the performance of this parameterized subfamily of estimators is illustrated for pair exchange ratio data sets.
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