Robustness of dual divergence estimators for models satisfying linear constraints

Aida Toma

doi:10.1016/j.crma.2013.02.005

Statistics

Robustness of dual divergence estimators for models satisfying linear constraints

Presented by: the Editorial Board

Aida Toma ^1,²

¹ Department of Applied Mathematics, Bucharest Academy of Economic Studies, Piaţa Romană 6, Bucharest, Romania
² “Gh. Mihoc–C. Iacob” Institute of Mathematical Statistics and Applied Mathematics, Romanian Academy, Calea 13 Septembrie 13, Bucharest, Romania

Comptes Rendus. Mathématique, Volume 351 (2013) no. 7-8, pp. 311-316.

Abstract
Résumé

We consider new classes of estimators and test statistics for models satisfying linear constraints with unknown parameter. These procedures are based on minimization of divergences through duality techniques. We prove that, for various divergences, the new approach provides robust estimation and test procedures, unlike the empirical likelihood method. We give general results using the influence function approach, which we exemplify in detail in the case of the Cressie–Read divergences. It is found that the Hellinger distance is one of the divergences that leads to robust procedures.

Nous considérons de nouvelles classes dʼestimateurs et de procédures de test pour des modèles satisfaisant des contraintes linéaires à paramètre inconnu. Ces procédures sont basées sur la minimisation des divergences grâce à des techniques de dualité. Nous prouvons que, pour de nombreuses divergences, la nouvelle approche fournit des estimateurs et des tests robustes, contrairement à la méthode de vraisemblance empirique. Nous donnons des résultats généraux en utilisant lʼapproche par fonction dʼinfluence, que nous illustrons en détail dans le cas des divergences de Cressie–Read. On remarque que la distance de Hellinger conduit à des procédures robustes.

Received: 2011-11-20
Accepted: 2013-02-12
Published online: 2013-04-01

DOI: 10.1016/j.crma.2013.02.005

Author's affiliations:

Aida Toma ^{1, 2}

¹ Department of Applied Mathematics, Bucharest Academy of Economic Studies, Piaţa Romană 6, Bucharest, Romania
² “Gh. Mihoc–C. Iacob” Institute of Mathematical Statistics and Applied Mathematics, Romanian Academy, Calea 13 Septembrie 13, Bucharest, Romania

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     title = {Robustness of dual divergence estimators for models satisfying linear constraints},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {311--316},
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     year = {2013},
     doi = {10.1016/j.crma.2013.02.005},
     language = {en},
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Aida Toma. Robustness of dual divergence estimators for models satisfying linear constraints. Comptes Rendus. Mathématique, Volume 351 (2013) no. 7-8, pp. 311-316. doi : 10.1016/j.crma.2013.02.005. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2013.02.005/

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