Multivariate moment based extreme value index estimators
| Autor: | Pauliina Ilmonen, Matias Heikkilä, Yves Dominicy |
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| Rok vydání: | 2016 |
| Předmět: |
Statistics and Probability
Multivariate statistics Generalization 05 social sciences Estimator Trimmed estimator 01 natural sciences Moment (mathematics) 010104 statistics & probability Computational Mathematics Minimum-variance unbiased estimator 0502 economics and business Statistics Affine invariant Rare events Extreme value index 0101 mathematics Statistics Probability and Uncertainty Minimax estimator Elliptical distribution Invariant estimator 050205 econometrics Mathematics |
| Zdroj: | Computational Statistics. 32:1481-1513 |
| ISSN: | 1613-9658 0943-4062 |
| Popis: | Modeling extreme events is of paramount importance in various areas of science — biostatistics, climatology, finance, geology, and telecommunications, to name a few. Most of these application areas involve multivariate data. Estimation of the extreme value index plays a crucial role in modeling rare events. There is an affine invariant multivariate generalization of the well known Hill estimator — the separating Hill estimator. However, the Hill estimator is only suitable for heavy tailed distributions. As in the case of the separating multivariate Hill estimator, we consider estimation of the extreme value index under the assumption of multivariate ellipticity. We provide affine invariant multivariate generalizations of the moment estimator and the mixed moment estimator. These estimators are suitable for both: light and heavy tailed distributions. Asymptotic properties of the new extreme value index estimators are derived under multivariate elliptical distribution with known location and scatter. The effect of replacing true location and scatter by estimates is examined in a thorough simulation study. |
| Databáze: | OpenAIRE |
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