Comptes Rendus
no. 6
Statistics
Minimum Hellinger distance estimators for some multivariate models: influence functions and breakdown point results
[Estimateurs de distance Hellinger minimum pour quelques modèles multivariées : fonctions d'influence et le point de rupture]

Présenté par : Paul Deheuvels

Aida Toma1
1 Mathematics Department, Academy of Economic Studies, Piaţa Romană 6, Bucharest, Romania
Comptes Rendus. Mathématique, Volume 345 (2007) no. 6, pp. 353-358.

Dans cette Note, nous étudions des propriétés de robustesse des estimateurs du minimum de la distance de Hellinger (MHDE) pour location et covariance dans le cas de quelques modèles multivariées. Nous déterminons la forme générale de la fonction d'influence du MHDE et établissons que, au modèle, elle est la même que la fonction d'influence de l'estimateur du maximum de vraisemblance. Nous démontrons également que, dans l'hypothèse du choix de la contamination la plus mauvaise, le point de rupture asymptotique du MHDE est superiéur à 1/2 au modèle.

In this Note we study robustness properties of the minimum Hellinger distance estimators (MHDE) for location and covariance in the case of some multivariate distributions. We determine the general form of the influence function of the MHDE and establish that, at the model, this is the same with the influence function of the maximum likelihood estimator. We also prove that, in the hypothesis of a worst possible choice of contamination, the asymptotic breakdown point of the MHDE is larger than 1/2 at the model.

Reçu le :
Accepté le :
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DOI : 10.1016/j.crma.2007.07.024
Aida Toma 1

1 Mathematics Department, Academy of Economic Studies, Piaţa Romană 6, Bucharest, Romania 
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Aida Toma. Minimum Hellinger distance estimators for some multivariate models: influence functions and breakdown point results. Comptes Rendus. Mathématique, Volume 345 (2007) no. 6, pp. 353-358. doi : 10.1016/j.crma.2007.07.024. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2007.07.024/

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