Ï-Divergence empirique et vraisemblance empirique gÃ©nÃ©ralisÃ©e

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Si on prend ε de l’ordre de n −3/2 log(n) −1 , le reste est de l’ordre de O(n −3/2 )(puisque T 1 n est bornée en probabilité et que T 0 n est déjà corrigé au sens deBartlett). La divergence est donc corrigeable au sens de Bartlett (au moinsjusqu’à l’ordre n −3/2 ).Références[1] Baggerly, K. A. Empirical likelihood as a goodness of fit measure.Biometrika 85 (1998), 535–547.[2] Bertail, P. Empirical likelihood in some nonparametric and semiparametricmodels, M.S. Nikulin, N. Balakrishnan, M. Mesbah and N.Limnios ed. 2004, ch. Parametric and Semiparametric Models with Applicationsto Reliability, Survival Analysis, and Quality of Life.[3] Bertail, P. Empirical likelihood in some semi-parametric models. Bernoulli12, 2 (2006).[4] Bertail, P., Harari-Kermadec, H., and Ravaille, D.γ−Divergence empirique et vraisemblance empirique généralisée. Documentde travail du CREST, 2004.[5] Bonnal, H., and Renault, E. On the efficient use of the informationalcontent of estimating equations : Implied probabilities and euclideanempirical likelihood. Cahiers scientifiques (CIRANO), 2004s-18, 2004.[6] Borwein, J. M., and Lewis, A. S. Duality relationships for entropylike minimization problem. SIAM Journal on Computation andOptimization 29, 2 (1991), 325–338.[7] Broniatowski, M., and Kéziou, A. Parametric estimation and teststhrough divergences. PhD thesis, L.S.T.A., 2003.[8] Chistyakov, G. P., and Götze, F. Moderate deviations for Student’sstatistic. Theory of Probability & Its Applications 47, 3 (2003),415–428.[9] Corcoran, S. A. Bartlett adjustment of empirical discrepancy statistics.Biometrika 85, 4 (1998), 967–972.[10] Cressie, N., and Read, T. R. C. Multinomial goodness-of-fit tests.Journal of the Royal Statistical Society, Series B 46, 3 (1984), 440–464.[11] Csiszár, I. Information type measures of difference of probability distributionsand indirect observations. Studia Scientiarum MathematicarumHungarica 2 (1967), 299–318.23
[12] Deville, J. C., and Sarndal, C. E. Calibration estimators in surveysampling. Journal of the American Statistical Association 87 (1992),376–382.[13] DiCiccio, T., Hall, P., and Romano, J. Empirical likelihood isbartlett-correctable. Annals of statistics 19, 2 (1991), 1053–1061.[14] DiCiccio, T., and Romano, J. Nonparametric confidence limits byresampling methods and least favorable families. International StatisticalReview 58 (1990), 59–76.[15] Efron, B. Student’s t-test under symmetry conditions. Journal ofamerican statistical society 64 (1969), 1278–1302.[16] Embrechts, P., Lindskog, F., and McNeil, A. J. Handbook ofheavy tailed distributions in finance. Elsevier, 2003, ch. Modelling dependencewith copulas and applications to risk management. edited byRachev ST.[17] Golan, A., Judge, G., and Miller, D. Maximum Entropy Econometrics.Wiley, New York, 1996.[18] Hartley, H. O., and Rao, J. N. K. A new estimation theory forsample surveys. Biometrika 55 (1968), 547–557.[19] Jing, B.-Y., and Wang, Q. An exponential nonuniform Berry-Esseenbound for self-normalized sums. Annals of Probability 27, 4 (1999), 2068–2088.[20] Jing, B. Y., and Wood, A. T. A. Exponential empirical likelihoodis not bartlett correctable. Annals of Statistics 24 (1996), 365–369.[21] Liese, F., and Vajda, I. Convex Statistical distance. Teubner, Leipzig,1987.[22] Léonard, C. Minimizers of energy functionals. Acta MathematicaHungarica 93, 4 (2001), 281–325.[23] Mykland, P. A. Bartlett type of identities. Annals of Statistics 22(1994), 21–38.[24] Mykland, P. A. Dual likelihood. Annals of Statistics 23 (1995),396–421.[25] Newey, W. K., and Smith, R. J. Higher order properties of GMMand generalized empirical likelihood estimators. Econometrica 72, 1(2004), 219–255.[26] Owen, A. B. Empirical likelihood ratio confidence intervals for a singlefunctional. Biometrika 75, 2 (1988), 237–249.24
Page 5 and 6: Propriétés 2.1(a) Par définition
Page 7 and 8: 3 Extension de la méthode de vrais
Page 9 and 10: s’explique en partie par le théo
Page 12 and 13: c’est-à-dire, en explicitant I
Page 14 and 15: Malheureusement les différentes pr
Page 16 and 17: Fig. 1 - Zones de confiance pour 4
Page 18 and 19: 5 ConclusionCe travail généralise
Page 20 and 21: BDémonstrations des résultatsB.1
Page 22 and 23: De même, en effectuant un dévelop
Page 26: [27] Owen, A. B. Empirical likeliho

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