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
[Robustesse des estimateurs par divergence duale pour des modèles satisfaisant des contraintes linéaires]

Présenté par : 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.

Résumé
Abstract

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.

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.

Reçu le : 2011-11-20
Accepté le : 2013-02-12
Publié le : 2013-04-01

DOI : 10.1016/j.crma.2013.02.005

Affiliations des auteurs :

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

@article{CRMATH_2013__351_7-8_311_0,
     author = {Aida Toma},
     title = {Robustness of dual divergence estimators for models satisfying linear constraints},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {311--316},
     publisher = {Elsevier},
     volume = {351},
     number = {7-8},
     year = {2013},
     doi = {10.1016/j.crma.2013.02.005},
     language = {en},
}

TY  - JOUR
AU  - Aida Toma
TI  - Robustness of dual divergence estimators for models satisfying linear constraints
JO  - Comptes Rendus. Mathématique
PY  - 2013
SP  - 311
EP  - 316
VL  - 351
IS  - 7-8
PB  - Elsevier
DO  - 10.1016/j.crma.2013.02.005
LA  - en
ID  - CRMATH_2013__351_7-8_311_0
ER  -

%0 Journal Article
%A Aida Toma
%T Robustness of dual divergence estimators for models satisfying linear constraints
%J Comptes Rendus. Mathématique
%D 2013
%P 311-316
%V 351
%N 7-8
%I Elsevier
%R 10.1016/j.crma.2013.02.005
%G en
%F CRMATH_2013__351_7-8_311_0

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/

Bibliographie
Cité par

[1] S. Bouzebda; A. Keziou New estimates and tests of independence in semiparametric copula models, Kybernetika, Volume 46 (2010), pp. 178-201

[2] M. Broniatowski; A. Keziou Minimization of ϕ-divergences on sets of signed measures, Stud. Sci. Math. Hung., Volume 43 (2006), pp. 403-442

[3] M. Broniatowski; A. Keziou Parametric estimation and tests through divergences and the duality technique, J. Multivar. Anal., Volume 100 (2009), pp. 16-31

[4] M. Broniatowski; A. Keziou Divergences and duality for estimation and test under moment condition models, J. Stat. Plan. Infer., Volume 142 (2012), pp. 2554-2573

[5] M. Broniatowski; S. Leorato An estimation method for Neyman chi-square divergence with application to test of hypothesis, J. Multivar. Anal., Volume 97 (2006), pp. 1409-1436

[6] M. Broniatowski; A. Toma; I. Vajda Decomposable pseudodistances and applications in statistical estimation, J. Stat. Plan. Infer., Volume 142 (2012), pp. 2574-2585

[7] N. Cressie; T.R.C. Read Multinomial goodness-of-fit tests, J. R. Stat. Soc. Ser. B, Volume 46 (1984), pp. 440-464

[8] N.L. Glenn; Y. Zhao Weighted empirical likelihood estimates and their robustness properties, Comput. Stat. Data An., Volume 51 (2007), pp. 5130-5141

[9] F.R. Hampel; E. Ronchetti; P.J. Rousseeuw; W. Stahel Robust Statistics: the Approach Based on Influence Functions, Wiley, New York, 1986

[10] A. Keziou Dual representation of ϕ-divergences and applications, C. R. Acad. Sci. Paris, Ser. I, Volume 336 (2003), pp. 857-862

[11] A.B. Owen Empirical Likelihood, Chapman & Hall CRC, 2001

[12] J. Qin; J. Lawless Empirical likelihood and general estimating equations, Ann. Statist., Volume 22 (1994), pp. 300-325

[13] A. Toma; M. Broniatowski Dual divergence estimators and tests: Robustness results, J. Multivar. Anal., Volume 102 (2011), pp. 20-36

[14] A. Toma; S. Leoni-Aubin Robust tests based on dual divergence estimators and saddlepoint approximations, J. Multivar. Anal., Volume 101 (2010), pp. 1143-1155

Cité par Sources :

Commentaires - Politique