Conditional principles for random weighted measures

ESAIM - Probability and Statistics

Volumn 9, Issue , 2005, Pages 283-306

  Gozlan, Nathael ^a  

^a UNIVERSITÉ PARIS OUEST NANTERRE LA DÉFENSE   (France)

Author keywords

Conditional laws of large numbers; Large deviations; Minimum entropy methods; Transportation cost inequalities

Indexed keywords

EID: 84996128548     PISSN: 12928100     EISSN: 12623318     Source Type: Journal    
DOI: 10.1051/ps:2005016     Document Type: Article

References (25)

1. S.G. Bobkov and F. Gotze, Exponential integrability and transportation cost related to logarithmic sobolev inequalities. J. Funct. Anal. 163 (1999) 1-28.
2. J.M. Borwein and A.S. Lewis, Duality relationships for entropy-like minimization problems. SIAM J. Control Optim. 29 (1991) 325-338.
3. J.M. Borwein and A.S. Lewis, Partially-finite programming in Li and the exitence of maximum entropy estimates. SIAM J. Optim.. 3 (1993) 248-267.
4. P. Cattiaux and N. Gozlan, Deviations lower bounds and conditional principles. Prepublications de l’Universite Paris 10, Nanterre (2002).
5. I. Csiszar, I-divergence geometry of probability distributions and minimization problems. Ann. Prob. 3 (1975) 146-158.
6. I. Csiszar, Sanov property, generalized I-projection and a conditional limit theorem. Ann. Prob. 12 (1984) 768-793.
7. I. Csiszar, Why least squares and maximum entropy? An axiomatic approach to inference for linear inverse problems. Ann. Statist. 19 (1991) 2032-2066.
8. I. Csiszar, F. Gamboa and E. Gassiat, Mem pixel correlated solutions for generalized moment and interpolation problems. IEEE Trans. Inform. Theory 45 (1999) 2253-2270.
9. D. Dacunha-Castelle and F. Gamboa, Maximum d’entropie et problemes des moments. Ann. Inst. Henri Poincaré 26 (1990) 567-596.
10. A. Dembo and O. Zeitouni, Large deviations techniques and applications. Second edition. Springer-Verlag (1998).
11. J. D. Deuschel and D.W. Stroock, Large deviations. Academic Press (1989).
12. R.S. Ellis, J. Gough and J.V. Pule, The large deviation principle for measures with random weights. Rev. Math. Phys. 5 (1993) 659-692.
13. F. Gamboa, Méthode du maximum d’entropie sur la moyenne et applications. These Orsay (1989).
14. F. Gamboa and E. Gassiat, Maximum d’entropie et problemes des moments: Cas multidimensionnel. Probab. Math. Statist. 12 (1991) 67-83.
15. F. Gamboa and E. Gassiat, Bayesian methods and maximum entropy for ill-posed inverse problems. Ann. Statist. 25 (1997) 328-350.
16. N. Gozlan, Principe conditionnel de Gibbs pour des contraintes fines approchées et inegalités de transport. Universite Paris 10-Nanterre (2005).
17. J.B. Hirriart-Urruty and C. Lemarechal, Fundamentals of convex analysis. Springer-Verlag (2001).
18. C. Leonard, Minimizer of energy functionals. Acta Math. Hungar. 93 (2001) 281-325.
19. C. Leonard, A convex optimization problem arising from probabilistic questions. Prepublications de l’Universite Paris 10-Nanterre (2004).
20. C. Leonard, Dominating points and entropic projections. Prepublications de l’Universite Paris 10-Nanterre (2004).
21. P. Massart, Saint-Flour Lecture Notes (2003).
22. J. Najim, A Cramer type theorem for weighted random variables. Electronic J. Probab. 7 (2002).
23. R.T. Rockafellar and R. Wets, Variational Analysis. Springer-Verlag (1997).
24. D. W. Stroock and O. Zeitouni, Microcanonical distributions, Gibbs states and the equivalence of ensembles, R. Durret and H. Kesten Eds., Birkhauser. Festschrift in honour of F. Spitzer (1991) 399-424.
25. A. Van Der Vaart and J. Wellner, Weak convergence and empirical processes. Springer Series in Statistics. Springer (1995).