Maximum likelihood principle and -divergence: discrete time observations

Jiří Michálek

Kybernetika (1998)

  • Volume: 34, Issue: 3, page [265]-288
  • ISSN: 0023-5954

Abstract

top
The paper investigates the relation between maximum likelihood and minimum -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.

How to cite

top

Michálek, Jiří. "Maximum likelihood principle and $I$-divergence: discrete time observations." Kybernetika 34.3 (1998): [265]-288. <http://eudml.org/doc/33354>.

@article{Michálek1998,
abstract = {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.},
author = {Michálek, Jiří},
journal = {Kybernetika},
keywords = {maximum likelihood estimate; information divergence; exponential families; discrete time process; autoregressive sequences; maximum likelihood estimate; information divergence; exponential families; discrete time process; autoregressive sequences},
language = {eng},
number = {3},
pages = {[265]-288},
publisher = {Institute of Information Theory and Automation AS CR},
title = {Maximum likelihood principle and $I$-divergence: discrete time observations},
url = {http://eudml.org/doc/33354},
volume = {34},
year = {1998},
}

TY - JOUR
AU - Michálek, Jiří
TI - Maximum likelihood principle and $I$-divergence: discrete time observations
JO - Kybernetika
PY - 1998
PB - Institute of Information Theory and Automation AS CR
VL - 34
IS - 3
SP - [265]
EP - 288
AB - 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.
LA - eng
KW - maximum likelihood estimate; information divergence; exponential families; discrete time process; autoregressive sequences; maximum likelihood estimate; information divergence; exponential families; discrete time process; autoregressive sequences
UR - http://eudml.org/doc/33354
ER -

References

top
  1. Anderson T. W., The Statistical Analysis of Time Series, Wiley, New York 1971 Zbl0835.62074MR0283939
  2. Basseville M., Benveniste A., Detection of Abrupt Changes in Signals and Dynamical Systems, Springer–Verlag, Berlin 1986 Zbl0578.93056
  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 (1988) 
  4. Kullback S., Information Theory and Statistics (in Russian), Nauka, Moscow 1967. Translated from the English original (1967) 
  5. Kupperman M., Further application of information theory to multivariate analysis and statistical inference, Ann. Math. Statist. 27 (1956), 1184 (1956) 
  6. Kűchler V., Sorensen M., 10.2307/1403382, Internat. Statist. Rev. (1989), 123–144 (1989) DOI10.2307/1403382
  7. Michálek J., Yule–Walker estimates and asymptotic -divergence rate, Problems Control Inform. Theory 19 (1990), 5–6, 387–398 (1990) Zbl0744.62126MR1086831
  8. Michálek J., A method of detecting changes in the behaviour of locally stationary sequences, Kybernetika 31 (1995), 1, 17–29 (1995) Zbl0868.62070MR1324658
  9. Morales D., Pardo L., Vajda I., About classical and some new statistics for testing hypothesis in parametric models, J. Multivariate Anal. (to appear) MR1467878
  10. Page E., 10.1093/biomet/41.1-2.100, Biometrika 41 (1954), 100–115 (1954) Zbl0056.38002MR0088850DOI10.1093/biomet/41.1-2.100

NotesEmbed ?

top

You must be logged in to post comments.