no. 9
Statistics
On Bayesian estimation via divergences
[Sur l'estimation bayésienne via les divergences]

Présenté par : the Editorial Board

Cherfi, Mohamed1
1 Laboratoire de mathématiques et applications, Département de mathématiques, Faculté des sciences, Université Hassiba-Benbouali de Chlef, 02000 Chlef, Algeria
Comptes Rendus. Mathématique, Tome 352 (2014) no. 9, pp. 749-754.

Dans cette Note, nous introduisons une nouvelle méthodologie d'inférence bayésienne en utilisant les ϕ-divergences et la technique de dualité. Nous obtenons les lois asymptotiques des estimateurs.

In this note, we introduce a new methodology for Bayesian inference through the use of ϕ-divergences and of the duality technique. The asymptotic laws of the estimates are established.

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/j.crma.2014.06.013
Cherfi, Mohamed 1

1 Laboratoire de mathématiques et applications, Département de mathématiques, Faculté des sciences, Université Hassiba-Benbouali de Chlef, 02000 Chlef, Algeria 
@article{CRMATH_2014__352_9_749_0,
     author = {Cherfi, Mohamed},
     title = {On {Bayesian} estimation via divergences},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {749--754},
     publisher = {Elsevier},
     volume = {352},
     number = {9},
     year = {2014},
     doi = {10.1016/j.crma.2014.06.013},
     language = {en},
     url = {http://www.numdam.org/articles/10.1016/j.crma.2014.06.013/}
}
TY  - JOUR
AU  - Cherfi, Mohamed
TI  - On Bayesian estimation via divergences
JO  - Comptes Rendus. Mathématique
PY  - 2014
SP  - 749
EP  - 754
VL  - 352
IS  - 9
PB  - Elsevier
UR  - http://www.numdam.org/articles/10.1016/j.crma.2014.06.013/
DO  - 10.1016/j.crma.2014.06.013
LA  - en
ID  - CRMATH_2014__352_9_749_0
ER  - 
%0 Journal Article
%A Cherfi, Mohamed
%T On Bayesian estimation via divergences
%J Comptes Rendus. Mathématique
%D 2014
%P 749-754
%V 352
%N 9
%I Elsevier
%U http://www.numdam.org/articles/10.1016/j.crma.2014.06.013/
%R 10.1016/j.crma.2014.06.013
%G en
%F CRMATH_2014__352_9_749_0
Cherfi, Mohamed. On Bayesian estimation via divergences. Comptes Rendus. Mathématique, Tome 352 (2014) no. 9, pp. 749-754. doi : 10.1016/j.crma.2014.06.013. http://www.numdam.org/articles/10.1016/j.crma.2014.06.013/

[1] Bouzebda, S.; Cherfi, M. General bootstrap for dual ϕ-divergence estimates, J. Probab. Stat. (2012), p. 33 p. (article ID 834107)

[2] Bouzebda, S.; Cherfi, M. Dual divergence estimators of the tail index, ISRN Probab. Stat. (2012), p. 14 p. (article ID 746203)

[3] Bouzebda, S.; Keziou, A. New estimates and tests of independence in semiparametric copula models, Kybernetika, Volume 46 (2010) no. 1, pp. 178-201

[4] Broniatowski, M.; Keziou, A. Minimization of ϕ-divergences on sets of signed measures, Studia Sci. Math. Hung., Volume 43 (2006) no. 4, pp. 403-442

[5] Broniatowski, M.; Keziou, A. Parametric estimation and tests through divergences and the duality technique, J. Multivar. Anal., Volume 100 (2009) no. 1, pp. 16-36

[6] Broniatowski, M.; Vajda, I. Several applications of divergence criteria in continuous families, Kybernetika, Volume 48 (2012) no. 4, pp. 600-636

[7] Cherfi, M. Dual divergences estimation for censored survival data, J. Stat. Plan. Inference, Volume 142 (2012) no. 7, pp. 1746-1756

[8] Chernozhukov, V.; Hong, H. An MCMC approach to classical estimation, J. Econometrics, Volume 115 (2003), pp. 293-346

[9] Cressie, N.; Read, T.R.C. Multinomial goodness-of-fit tests, J. R. Stat. Soc., Ser. B, Stat. Methodol., Volume 46 (1984) no. 3, pp. 440-464

[10] Dey, D.K.; Birmiwal, L.R. Robust Bayesian analysis using divergence measures, Stat. Probab. Lett., Volume 20 (1994) no. 4, pp. 287-294

[11] Hanousek, J. Robust Bayesian type estimators and their asymptotic representation, Stat. Decis., Volume 8 (1990) no. 1, pp. 61-69

[12] Hanousek, J. Generalized Bayesian-type estimators. Robust and sensitivity analysis, Kybernetika, Volume 30 (1994) no. 3, pp. 271-278

[13] Hooker, G.; Vidyashankar, A. Bayesian model robustness via disparities, Test (2014) (in press) | DOI

[14] Ibragimov, I.A.; Has'minskii, R.Z. Statistical Estimation — Asymptotic Theory, Springer-Verlag, New York, 1981

[15] Keziou, A. Dual representation of ϕ-divergences and applications, C. R. Acad. Sci. Paris, Ser. I, Volume 336 (2003) no. 10, pp. 857-862

[16] Keziou, A.; Leoni-Aubin, S. On empirical likelihood for semiparametric two-sample density ratio models, J. Stat. Plan. Inference, Volume 138 (2008) no. 4, pp. 915-928

[17] Lehmann, E.L.; Casella, G. Theory of Point Estimation, Springer Texts in Statistics, Springer-Verlag, New York, 1998

[18] Liese, F.; Vajda, I. Convex Statistical Distances, Teubner-Texte zur Mathematik [Teubner Texts in Mathematics], vol. 95, BSB B. G. Teubner Verlagsgesellschaft, Leipzig, Germany, 1987 (with German, French and Russian summaries)

[19] Liese, F.; Vajda, I. On divergences and informations in statistics and information theory, IEEE Trans. Inf. Theory, Volume 52 (2006) no. 10, pp. 4394-4412

[20] Lindsay, B.G. Efficiency versus robustness: the case for minimum Hellinger distance and related methods, Ann. Statist., Volume 22 (1994) no. 2, pp. 1081-1114

[21] Pardo, L. Statistical Inference Based on Divergence Measures, Statistics: Textbooks and Monographs, vol. 185, Chapman & Hall/CRC, Boca Raton, FL, USA, 2006

[22] F. Peng, D. Dey, Bayesian analysis of outlier problems using divergence measures, Canad. J. Statist. 23 (2), 199–213.

[23] G. Ragusa, Bayesian properties of minimum divergence and generalized empirical likelihood methods, Unpublished manuscript, 2006.

[24] Robert, C. The Bayesian Choice: From Decision-Theoretic Foundations to Computational Implementations, Springer, New York, 2001

[25] Robert, C.P.; Casella, G. Monte Carlo Statistical Methods, Springer, New York, 2005

[26] Strasser, H. Consistency of maximum likelihood and Bayes estimates, Ann. Statist., Volume 9 (1981), pp. 1107-1113

[27] Tian, L.; Liu, J.S.; Wei, L.J. Implementation of estimating-function based inference procedures with Markov chain Monte Carlo samplers, J. Amer. Statist. Assoc., Volume 102 (2007), pp. 881-888

[28] Toma, A.; Broniatowski, M. Dual divergence estimators and tests: robustness results, J. Multivar. Anal., Volume 102 (2011) no. 1, pp. 20-36

[29] Toma, A.; Leoni-Aubin, S. Robust tests based on dual divergence estimators and saddlepoint approximations, J. Multivar. Anal., Volume 101 (2010) no. 5, pp. 1143-1155

[30] van der Vaart, A.W. Asymptotic Statistics, Cambridge Series in Statistical and Probabilistic Mathematics, vol. 3, Cambridge University Press, Cambridge, UK, 1998

Cité par Sources :