# Asymptotic Rényi distances for random fields: properties and applications

Kybernetika (1999)

- Volume: 35, Issue: 4, page [507]-525
- ISSN: 0023-5954

## Access Full Article

top## Abstract

top## How to cite

topJanžura, Martin. "Asymptotic Rényi distances for random fields: properties and applications." Kybernetika 35.4 (1999): [507]-525. <http://eudml.org/doc/33444>.

@article{Janžura1999,

abstract = {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.},

author = {Janžura, Martin},

journal = {Kybernetika},

keywords = {statistical inference},

language = {eng},

number = {4},

pages = {[507]-525},

publisher = {Institute of Information Theory and Automation AS CR},

title = {Asymptotic Rényi distances for random fields: properties and applications},

url = {http://eudml.org/doc/33444},

volume = {35},

year = {1999},

}

TY - JOUR

AU - Janžura, Martin

TI - Asymptotic Rényi distances for random fields: properties and applications

JO - Kybernetika

PY - 1999

PB - Institute of Information Theory and Automation AS CR

VL - 35

IS - 4

SP - [507]

EP - 525

AB - 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.

LA - eng

KW - statistical inference

UR - http://eudml.org/doc/33444

ER -

## References

top- Csiszár I., Information–type measures of difference of probability distributions and indirect observations, Stud. Sci. Math. Hungar. 2 (1967), 299–318 (1967) Zbl0157.25802MR0219345
- Dembo A., Zeitouni O., Large Deviations Techniques and Applications, Jones and Bartlett Publishers, Boston 1993 Zbl0896.60013MR1202429
- Georgii H. O., Gibbs Measures and Place Transitions, De Gruyter, Berlin 1988 MR0956646
- 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 (1987) MR0956688
- 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 (1994) MR1311947
- Janžura M., On the concept of asymptotic Rényi distances for random fields, Kybernetika 5 (1999), 3, 353–366 (1999)
- Liese F., Vajda I., Convex Statistical Problems, Teubner, Leipzig 1987 MR0926905
- Perez A., Risk estimates in terms of generalized $f$–entropies, In: Proc. Coll. on Inform. Theory (A. Rényi, ed.), Budapest 1968 MR0263542
- 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 (1961) MR0132570
- Vajda I., 10.1007/BF02018663, Period. Math. Hungar. 2 (1972), 223–234 (1972) Zbl0248.62001MR0335163DOI10.1007/BF02018663
- Vajda I., The Theory of Statistical Inference and Information, Kluwer, Dordrecht – Boston – London 1989
- Younès L., 10.1007/BF00341287, Probab. Theory Related Fields 82 (1989), 625–645 (1989) MR1002904DOI10.1007/BF00341287

## NotesEmbed ?

topTo embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.