Mixed moment estimator and location invariant alternatives

A new class of estimators of the extreme value index is developed. It has a simple form and is asymptotically very close to the maximum likelihood estimator for a wide class of heavy-tailed models. We also propose an alternative class of estimators, dependent on a tuning parameter p  ∈ (0,1) and inv...

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Bibliographic Details
Published inExtremes (Boston) Vol. 12; no. 2; pp. 149 - 185
Main Authors Fraga Alves, M. Isabel, Gomes, M. Ivette, de Haan, Laurens, Neves, Cláudia
Format Journal Article
LanguageEnglish
Published Boston Springer US 01.06.2009
Springer Nature B.V
Subjects
Civil Engineering
Economics
Environmental Management
Estimating techniques
Finance
Hydrogeology
Insurance
Management
Mathematics and Statistics
Measures of variability
Monte Carlo simulation
Quality Control
Random variables
Reliability
Safety and Risk
Statistics
Statistics for Business
Studies
Value analysis
Semi-parametric estimation
62E20; Secondary—65C05
Primary—62G32
Statistics of extremes
Extreme value index
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Summary:A new class of estimators of the extreme value index is developed. It has a simple form and is asymptotically very close to the maximum likelihood estimator for a wide class of heavy-tailed models. We also propose an alternative class of estimators, dependent on a tuning parameter p  ∈ (0,1) and invariant for changes in both scale and/or location. Such a tuning parameter can help us to choose the number of top order statistics to be used in the estimation of extreme parameters.
ISSN:1386-1999
1572-915X
DOI:10.1007/s10687-008-0073-3