| Title:
|
Asymptotic Rényi distances for random fields: properties and applications (English) |
| Author:
|
Janžura, Martin |
| Language:
|
English |
| Journal:
|
Kybernetika |
| ISSN:
|
0023-5954 |
| Volume:
|
35 |
| Issue:
|
4 |
| Year:
|
1999 |
| Pages:
|
[507]-525 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
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. (English) |
| Keyword:
|
statistical inference |
| MSC:
|
60F10 |
| MSC:
|
60G60 |
| MSC:
|
62B10 |
| MSC:
|
62M40 |
| idZBL:
|
Zbl 1274.62062 |
| idMR:
|
MR1723573 |
| . |
| Date available:
|
2009-09-24T19:27:46Z |
| Last updated:
|
2015-03-27 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/135305 |
| . |
| Reference:
|
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| Reference:
|
[2] Dembo A., Zeitouni O.: Large Deviations Techniques and Applications.Jones and Bartlett Publishers, Boston 1993 Zbl 0896.60013, MR 1202429 |
| Reference:
|
[3] Georgii H. O.: Gibbs Measures and Place Transitions.De Gruyter, Berlin 1988 MR 0956646 |
| Reference:
|
[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 0956688 |
| Reference:
|
[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 1311947 |
| Reference:
|
[6] Janžura M.: On the concept of asymptotic Rényi distances for random fields.Kybernetika 5 (1999), 3, 353–366 |
| Reference:
|
[7] Liese F., Vajda I.: Convex Statistical Problems.Teubner, Leipzig 1987 MR 0926905 |
| Reference:
|
[8] Perez A.: Risk estimates in terms of generalized $f$–entropies.In: Proc. Coll. on Inform. Theory (A. Rényi, ed.), Budapest 1968 MR 0263542 |
| Reference:
|
[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 0132570 |
| Reference:
|
[10] Vajda I.: On the $f$–divergence and singularity of probability measures.Period. Math. Hungar. 2 (1972), 223–234 Zbl 0248.62001, MR 0335163, 10.1007/BF02018663 |
| Reference:
|
[11] Vajda I.: The Theory of Statistical Inference and Information.Kluwer, Dordrecht – Boston – London 1989 |
| Reference:
|
[12] Younès L.: Parametric inference for imperfectly observed Gibbsian fields.Probab. Theory Related Fields 82 (1989), 625–645 MR 1002904, 10.1007/BF00341287 |
| . |
