| Title:
|
Maximum likelihood principle and $I$-divergence: discrete time observations (English) |
| Author:
|
Michálek, Jiří |
| Language:
|
English |
| Journal:
|
Kybernetika |
| ISSN:
|
0023-5954 |
| Volume:
|
34 |
| Issue:
|
3 |
| Year:
|
1998 |
| Pages:
|
[265]-288 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
The paper investigates the relation between maximum likelihood and minimum $I$-divergence estimates of unknown parameters and studies the asymptotic behaviour of the likelihood ratio maximum. Observations are assumed to be done in the discrete time. (English) |
| Keyword:
|
maximum likelihood estimate |
| Keyword:
|
information divergence |
| Keyword:
|
exponential families |
| Keyword:
|
discrete time process |
| Keyword:
|
autoregressive sequences |
| MSC:
|
62B10 |
| MSC:
|
62F12 |
| MSC:
|
62M10 |
| idZBL:
|
Zbl 1274.62066 |
| idMR:
|
MR1640966 |
| . |
| Date available:
|
2009-09-24T19:16:09Z |
| Last updated:
|
2015-03-28 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/135207 |
| . |
| Related article:
|
http://dml.cz/handle/10338.dmlcz/135208 |
| . |
| Reference:
|
[1] Anderson T. W.: The Statistical Analysis of Time Series.Wiley, New York 1971 Zbl 0835.62074, MR 0283939 |
| Reference:
|
[2] Basseville M., Benveniste A.: Detection of Abrupt Changes in Signals and Dynamical Systems.Springer–Verlag, Berlin 1986 Zbl 0578.93056 |
| Reference:
|
[3] Krishnaiah P. R., Miao B. Q.: Review about estimation of change points.In: Handbook of Statistics (P. R. Krishnaiah and C. R. Rao, eds.), Elsevier Sci. Publishers, Amsterdam 1988, Vol. 7, pp. 375–402 |
| Reference:
|
[4] Kullback S.: Information Theory and Statistics (in Russian).Nauka, Moscow 1967. Translated from the English original |
| Reference:
|
[5] Kupperman M.: Further application of information theory to multivariate analysis and statistical inference.Ann. Math. Statist. 27 (1956), 1184 |
| Reference:
|
[6] Kűchler V., Sorensen M.: Exponential families of stochastic processes: A unifying semimartingale approach.Internat. Statist. Rev. (1989), 123–144 10.2307/1403382 |
| Reference:
|
[7] Michálek J.: Yule–Walker estimates and asymptotic $I$-divergence rate.Problems Control Inform. Theory 19 (1990), 5–6, 387–398 Zbl 0744.62126, MR 1086831 |
| Reference:
|
[8] Michálek J.: A method of detecting changes in the behaviour of locally stationary sequences.Kybernetika 31 (1995), 1, 17–29 Zbl 0868.62070, MR 1324658 |
| Reference:
|
[9] Morales D., Pardo L., Vajda I.: About classical and some new statistics for testing hypothesis in parametric models.J. Multivariate Anal. (to appear) MR 1467878 |
| Reference:
|
[10] Page E.: Continuous inspection schemes.Biometrika 41 (1954), 100–115 Zbl 0056.38002, MR 0088850, 10.1093/biomet/41.1-2.100 |
| . |
