Inference in families of distributions

Statistics

Volumn 45, Issue 3, 2011, Pages 223-236

  Pelletier, Bruno ^a  

^a UNIVERSITÉ RENNES 2   (France)

Author keywords

divergence; Empirical likelihood; Generalized moment; Maximum entropy; Parametric statistics

Indexed keywords

EID: 79957963204     PISSN: 02331888     EISSN: 10294910     Source Type: Journal    
DOI: 10.1080/02331880903546324     Document Type: Article

References (27)

1. O. Barndorff-Nielsen, Information and Exponential Families in Statistical Theory,Wiley Series in Probability and Mathematical Statistics, JohnWiley & Sons Ltd, Chichester, 1978.
2. J.M. Borwein and A.S. Lewis, Duality relationships for entropy-like minimization problems, SIAM J. Control and Optim. 29 (1991), pp. 325-338.
3. J.M. Borwein and A.S. Lewis, Partially-finite programming in L1 and the existence of maximum entropy estimates, SIAM J. Optim. 3 (1993), pp. 248-267.
4. J.M. Borwein and A.S. Lewis, On the failure of maximum entropy reconstruction for Fredholm equations and other infinite systems, Math. Program. 63 (1993), pp. 251-261.
5. D. Dacunha-Castelle and F. Gamboa, Maximum d'entropie et problèmes des moments, Ann. Insti. Henri Poincaré B 26 (1990), pp. 567-596.
6. A. Decarreau, D. Hilhorst, C. Lemaréchal and J. Navaza, Dual methods in entropy maximization. Application to some problems in crystallography, SIAM J. on Optim. 2 (1992), pp. 173-197.
7. F. Gamboa and E. Gasiat, Bayesian methods and maximum entropy for ill-posed inverse problems, Ann. Stat. 25 (1997), pp. 328-350.
8. I. Csiszár, Generalized projections for non-negative functions, Acta Math. Hung. 68 (1995), pp. 161-186.
9. C. Léonard, Minimizers of energy functionals under not very integrable constraints, J. Convex Anal. 10 (2003), pp. 63-88.
10. D. Dacunha-Castelle and F. Gamboa, Maximum d'entropie, fonctions de type négatif et généralisation des familles exponentielles, Université d'Orsay, France, Prépublications.
11. P. McCullagh and J.A. Nelder, Generalized Linear Models, Monographs on Statistics and Applied Probability, Chapman & Hall, London, 1983.
12. J.A. Pardo and M.C. Pardo, Minimum Φ-divergence estimator and Φ-divergence statistics in generalized linear models with binary data, Meth. Comput. Appl. Probab. 10 (2008), pp. 357-379.
13. F. Liese and I. Vajda, Convex Statistical Distances, Teubner Texts in Mathematics, Vol. 95, BSB B.G. Teubner Verlagsgesellschaft, Leipzig, 1987.
14. A. Keziou, Dual representation of Φ-divergence and applications, C. R. Math. Acad. Sci. Paris 336 (2003), pp. 857-862.
15. M. Broniatowski and A. Keziou, Minimization of Φ-divergences on sets of signed measures, Stud. Sci. Math. Hung. 43 (2006), pp. 403-442.
16. L. Pardo, Statistical Inference Based on Divergence Measures, Chapman & Hall/CRC, Boca Raton, FL, 2006.
17. A.B. Owen, Empirical likelihood ratio confidence intervals for a single functional, Biometrika 75 (1988), pp. 237-249.
18. A.B. Owen, Empirical Likelihood, Chapman and Hall, Boca Raton, FL, 2001.
19. P. Bertail, Empirical likelihood in some semiparametric models, Bernoulli 12 (2006), pp. 299-331.
20. M. Broniatowski, Estimation of the Kullback-Leibler divergence, Math. Methods Stat. 12 (2004), pp. 391-409.
21. R.T. Rockafellar, Convex Analysis, Princeton University Press, Princeton, NJ, 1970.
22. G.E. Bredon, Topology and Geometry, Graduate Texts in Mathematics, Vol. 139, Springer-Verlag, NewYork.
23. J. Dieudonné, Eléments d'Analyse, Tome I, Fondements de l'Analyse Moderne, Gauthier-Vilars, Paris, 1972.
24. J. Blot, On global implicit functions, Nonlinear Anal. Theory Methods Appl. 17 (1991), pp. 947-959.
25. A.W. van der Vaart, Asymptotic Statistics, Cambridge University Press, Cambridge, 1998.
26. S. van de Geer, Empirical Processes in M-Estimation, Cambridge University Press, Cambridge, 2000.
27. F. Zhang, The Schur Complement and its Applications, Numerical Methods and Algorithms, Vol. 4, Springer-Verlag, NewYork, 2005.