Closures of exponential families

Annals of Probability

Volumn 33, Issue 2, 2005, Pages 582-600

  Csiszár, Imre ^a   Matúš, František ^b,c  

^a INSTITUTE OF EXPERIMENTAL MEDICINE   (Hungary)

^b INSTITUTE OF MATHEMATICS   (Czech Republic)

^c INSTITUTE OF INFORMATION THEORY AND AUTOMATION   (Czech Republic)

Author keywords

Accessible face; Convex core; Convex support; Exponential family; Extension; Information divergence; Variation distance; Weak convergence

Indexed keywords

EID: 17044403041     PISSN: 00911798     EISSN: None     Source Type: Journal    
DOI: 10.1214/009117904000000766     Document Type: Article

References (12)

1. BARNDORFF-NIELSEN, O. (1978). Information and Exponential Families in Statistical Theory. Wiley, New York.
2. BROWN, L. D. (1986). Fundamentals of Statistical Exponential Families. IMS Lecture Notes Monogr. Ser. 9. Hayward, CA.
3. CHENTSOV, N. N. (1982). Statistical Decision Rules and Optimal Inference. Amer. Math. Soc., Providence, RI.
4. CSISZÁR, I. (1984). Sanov property, generalized I-projections, and a conditional limit theorem. Ann. Probab. 12 768-793.
5. CSISZÁR, I. and MATÚŠ, F. (2000). Information projections revisited. In Proc. 2000 IEEE International Symposium on Information Theory 490. IEEE, New York.
6. d. Studio Sci. Math. Hungar. 38 177-190.
7. CSISZÁR, I. and MATÚŠ, F. (2003). Information projections revisited. IEEE Trans. Inform. Theory 49 1474-1490.
8. CSISZÁR, I. and MATÚŠ, F. (2004). On information closures of exponential families: A counterexample. IEEE Trans. Inform. Theory 50 922-924.
9. HARREMOËS, P. (2002). The information topology. In Proc. 2002 IEEE International Symposium on Information Theory 431. IEEE, New York.
10. HIRIART-URRUTY, J.-B. and LEMARÉCHAL, C. (2001). Fundamentals of Convex Analysis. Springer, Berlin.
11. LETAC, G. (1992). Lectures on Natural Exponential Families and Their Variance Functions. Monografias de Matemática 50. Instituto de Matemática Pura e Aplicada, Rio de Janeiro, Brazil.
12. ROCKAFELLAR, R. T. (1970). Convex Analysis. Princeton Univ. Press.