Box-Cox transformation on the estimation of extreme value index (EVI) and high quantiles for heavy-tailed distributions under dependence serials - Archive ouverte HAL Accéder directement au contenu
Pré-Publication, Document De Travail Année : 2023

Box-Cox transformation on the estimation of extreme value index (EVI) and high quantiles for heavy-tailed distributions under dependence serials

Transformation de Box-Cox sur l'estimation de l'indice des valeurs extrêmes et de quantiles élevés pour des distributions à queues lourdes sous la dépendance serielle

Résumé

The Box-Cox transformation is used to make data more suitable for statistical analysis. Its application to extreme value statistics increases the convergence rate of some classical estimators of the tail index and reduces their bias in the context of independent and identically distributed (i.i.d.) random variables. In this paper, we study a bias-reducing estimator of the extreme value index under β-mixing serials dependence using the Box-Cox transformation. Under certain regular conditions, we establish the asymptotic normality of the proposed estimator and derive an asymptotically unbiased estimator of high quantiles. In a simulation study, we highlight the performance of our proposals, which we compare with alternative estimators recently introduced in the literature.
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Dates et versions

hal-04181113 , version 1 (14-08-2023)
hal-04181113 , version 2 (19-08-2023)

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  • HAL Id : hal-04181113 , version 2

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Mame Birame Diouf, Hadji Deme, Solym M Manou-Abi, Yousri Slaoui. Box-Cox transformation on the estimation of extreme value index (EVI) and high quantiles for heavy-tailed distributions under dependence serials. 2023. ⟨hal-04181113v2⟩
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