[Estimateurs de distance Hellinger minimum pour quelques modèles multivariées : fonctions d'influence et le point de rupture]
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.
Accepté le :
Publié le :
@article{CRMATH_2007__345_6_353_0,
author = {Toma, Aida},
title = {Minimum {Hellinger} distance estimators for some multivariate models: influence functions and breakdown point results},
journal = {Comptes Rendus. Math\'ematique},
pages = {353--358},
publisher = {Elsevier},
volume = {345},
number = {6},
year = {2007},
doi = {10.1016/j.crma.2007.07.024},
language = {en},
url = {http://www.numdam.org/articles/10.1016/j.crma.2007.07.024/}
}
TY - JOUR AU - Toma, Aida TI - Minimum Hellinger distance estimators for some multivariate models: influence functions and breakdown point results JO - Comptes Rendus. Mathématique PY - 2007 SP - 353 EP - 358 VL - 345 IS - 6 PB - Elsevier UR - http://www.numdam.org/articles/10.1016/j.crma.2007.07.024/ DO - 10.1016/j.crma.2007.07.024 LA - en ID - CRMATH_2007__345_6_353_0 ER -
%0 Journal Article %A Toma, Aida %T Minimum Hellinger distance estimators for some multivariate models: influence functions and breakdown point results %J Comptes Rendus. Mathématique %D 2007 %P 353-358 %V 345 %N 6 %I Elsevier %U http://www.numdam.org/articles/10.1016/j.crma.2007.07.024/ %R 10.1016/j.crma.2007.07.024 %G en %F CRMATH_2007__345_6_353_0
Toma, Aida. Minimum Hellinger distance estimators for some multivariate models: influence functions and breakdown point results. Comptes Rendus. Mathématique, Tome 345 (2007) no. 6, pp. 353-358. doi : 10.1016/j.crma.2007.07.024. http://www.numdam.org/articles/10.1016/j.crma.2007.07.024/
[1] Minimum disparity estimation in the continuous case: efficiency, distributions, robustness, Annals of the Institute of Statistical Mathematics, Volume 46 (1994), pp. 683-705
[2] Minimum negative exponential disparity estimation in parametric models, Journal of Statistical Planning and Inference, Volume 58 (1997), pp. 349-370
[3] Minimum Hellinger distance estimates for parametric models, Annals of Statistics, Volume 5 (1977), pp. 445-463
[4] Estimation through Kullback–Leibler divergence, Mathematical Methods of Statistics, Volume 12 (2003), pp. 391-409
[5] M. Broniatowski, A. Keziou, Parametric estimation and testing through divergences, Preprint 2004-1, L.S.T. A–Université Paris 6
[6] Efficiency versus robustness: the case of minimum Hellinger distance and related methods, Annals of Statistics, Volume 22 (1994), pp. 1081-1114
[7] Minimum disparity estimation: asymptotic normality and breakdown point results, Bulletin of Informatics and Cybernetics, Volume 99 (1999), pp. 1-15
[8] Minimum Hellinger distance estimation for the analysis of count data, Journal of the American Statistical Association, Volume 82 (1987), pp. 802-807
[9] Hellinger deviance tests: efficiency, breakdown points, and examples, Journal of the American Statistical Association, Volume 84 (1989), pp. 104-113
[10] Minimum Hellinger distance estimation for multivariate location and covariance, Journal of the American Statistical Association, Volume 81 (1986), pp. 223-229
[11] A. Toma, Minimum Hellinger distance estimators for multivariate distributions from Johnson system, Journal of Statistical Planning and Inference (2007), in press
Cité par Sources :
