Dans cet article, nous considérons le problème de l'estimation robuste de certains paramètres relatifs à une distribution multivariée lognormale. Dans ce but, nous construisons une classe d'estimateurs et donnons certaines de leurs propriétés telles que la consistence au sens de Fisher, la robustesse et la normalité asymptotique.
In this paper we consider the problem of robust estimation of some parameters related to a multivariate lognormal distribution. In this sense, we construct a class of estimators and discuss some of its properties, such as Fisher consistency, robustness and asymptotic normality.
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Aida Toma 1
@article{CRMATH_2004__338_9_723_0, author = {Aida Toma}, title = {Bounded influence estimators for multivariate lognormal distributions}, journal = {Comptes Rendus. Math\'ematique}, pages = {723--728}, publisher = {Elsevier}, volume = {338}, number = {9}, year = {2004}, doi = {10.1016/j.crma.2004.02.017}, language = {en}, }
Aida Toma. Bounded influence estimators for multivariate lognormal distributions. Comptes Rendus. Mathématique, Volume 338 (2004) no. 9, pp. 723-728. doi : 10.1016/j.crma.2004.02.017. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2004.02.017/
[1] Principal component analysis based on robust estimators of the covariance or correlation matrix: influence functions and efficiencies, Biometrika, Volume 87 (2000), pp. 603-618
[2] Asymptotic behavior of S-estimators of multivariate location parameters and dispersion matrices, Ann. Statist., Volume 15 (1987), pp. 1269-1292
[3] The notion of breakdown point (P.J. Bickel; K.A. Doksum; J.L. Hodges, eds.), A Festschrift for Erich L. Lechmann, Wadsworth, Belmont, CA, 1983
[4] Robust Statistics: The Approach Based on Influence Function, Wiley, 1986
[5] On UMVU estimators for the multivariate lognormal distribution and their variances, Comm. Statist. Theory Methods, Volume 11 (1982), pp. 687-697
[6] On the multivariate lognormal distribution, J. Industrial Math. Soc., Volume 16 (1966), pp. 63-76
[7] Multivariate Analysis, Academic Press, 1994
[8] Robust M-estimators of multivariate location and scatter, Ann. Statist., Volume 4 (1976), pp. 51-67
[9] Robust estimation of multivariate location and scatter (S. Kots; C. Read; D. Banks, eds.), Encyclopedia of Statistical Sciencies, Wiley, 1998
[10] Multivariate estimation with high breakdown point (W. Grossmann; G. Pflug; I. Vincze; W. Wertz, eds.), Math. Statist. Appl., vol. B, Reidel, Dodrecht, 1985, pp. 283-297
[11] Robust estimators for the parameters of multivariate lognormal distributions, Comm. Statist. Theory Methods, Volume 32 (2003), pp. 1405-1417
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