Geodesic
Asymptotic Rényi distances for random fields: properties and applications
Kybernetika, Tome 35 (1999) no. 4, pp. 507-525 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

Voir la notice de l'article

The approach introduced in Janžura [Janzura 1997] is further developed and the asymptotic Rényi distances are studied mostly from the point of their monotonicity properties. The results are applied to the problems of statistical inference.
The approach introduced in Janžura [Janzura 1997] is further developed and the asymptotic Rényi distances are studied mostly from the point of their monotonicity properties. The results are applied to the problems of statistical inference.
Classification : 60F10, 60G60, 62B10, 62M40
Keywords: statistical inference 
@article{KYB_1999_35_4_a8,
     author = {Jan\v{z}ura, Martin},
     title = {Asymptotic {R\'enyi} distances for random fields: properties and applications},
     journal = {Kybernetika},
     pages = {507--525},
     year = {1999},
     volume = {35},
     number = {4},
     mrnumber = {1723573},
     zbl = {1274.62062},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/KYB_1999_35_4_a8/}
}
TY  - JOUR
AU  - Janžura, Martin
TI  - Asymptotic Rényi distances for random fields: properties and applications
JO  - Kybernetika
PY  - 1999
SP  - 507
EP  - 525
VL  - 35
IS  - 4
UR  - http://geodesic.mathdoc.fr/item/KYB_1999_35_4_a8/
LA  - en
ID  - KYB_1999_35_4_a8
ER  - 
%0 Journal Article
%A Janžura, Martin
%T Asymptotic Rényi distances for random fields: properties and applications
%J Kybernetika
%D 1999
%P 507-525
%V 35
%N 4
%U http://geodesic.mathdoc.fr/item/KYB_1999_35_4_a8/
%G en
%F KYB_1999_35_4_a8
Janžura, Martin. Asymptotic Rényi distances for random fields: properties and applications. Kybernetika, Tome 35 (1999) no. 4, pp. 507-525. http://geodesic.mathdoc.fr/item/KYB_1999_35_4_a8/

[1] Csiszár I.: Information–type measures of difference of probability distributions and indirect observations. Stud. Sci. Math. Hungar. 2 (1967), 299–318 | MR | Zbl

[2] Dembo A., Zeitouni O.: Large Deviations Techniques and Applications. Jones and Bartlett Publishers, Boston 1993 | MR | Zbl

[3] Georgii H. O.: Gibbs Measures and Place Transitions. De Gruyter, Berlin 1988 | MR

[4] Janžura M.: Large deviations theorem for Gibbs random fields. In: Proc. 5th Pannonian Symp. on Math. Statist. (W. Grossmann, J. Mogyorodi, I. Vincze and W. Wertz, eds.), Akadémiai Kiadó, Budapest 1987, pp. 97–112 | MR

[5] Janžura M.: Asymptotic behaviour of the error probabilities in the pseudo–likelihood ratio test for Gibbs–Markov distributions. In: Asymptotic Statistics (P. Mandl and M. Hušková, eds.), Physica–Verlag 1994, pp. 285–296 | MR

[6] Janžura M.: On the concept of asymptotic Rényi distances for random fields. Kybernetika 5 (1999), 3, 353–366

[7] Liese F., Vajda I.: Convex Statistical Problems. Teubner, Leipzig 1987 | MR

[8] Perez A.: Risk estimates in terms of generalized $f$–entropies. In: Proc. Coll. on Inform. Theory (A. Rényi, ed.), Budapest 1968 | MR

[9] Rényi A.: On measure of entropy and information. In: Proc. 4th Berkeley Symp. Math. Statist. Prob., Univ of Calif. Press, Berkeley 1961, Vol. 1, pp. 547–561 | MR

[10] Vajda I.: On the $f$–divergence and singularity of probability measures. Period. Math. Hungar. 2 (1972), 223–234 | DOI | MR | Zbl

[11] Vajda I.: The Theory of Statistical Inference and Information. Kluwer, Dordrecht – Boston – London 1989

[12] Younès L.: Parametric inference for imperfectly observed Gibbsian fields. Probab. Theory Related Fields 82 (1989), 625–645 | DOI | MR