Maximum likelihood principle and I -divergence: continuous time observations

Jiří Michálek

Kybernetika (1998)

  • Volume: 34, Issue: 3, page [289]-308
  • ISSN: 0023-5954

Abstract

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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 continuous time.

How to cite

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Michálek, Jiří. "Maximum likelihood principle and $I$-divergence: continuous time observations." Kybernetika 34.3 (1998): [289]-308. <http://eudml.org/doc/33355>.

@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 continuous time.},
author = {Michálek, Jiří},
journal = {Kybernetika},
keywords = {maximum likelihood estimation; information divergence; Gaussian process; autoregressive processes; maximum likelihood estimation; information divergence; Gaussian process; autoregressive processes},
language = {eng},
number = {3},
pages = {[289]-308},
publisher = {Institute of Information Theory and Automation AS CR},
title = {Maximum likelihood principle and $I$-divergence: continuous time observations},
url = {http://eudml.org/doc/33355},
volume = {34},
year = {1998},
}

TY - JOUR
AU - Michálek, Jiří
TI - Maximum likelihood principle and $I$-divergence: continuous time observations
JO - Kybernetika
PY - 1998
PB - Institute of Information Theory and Automation AS CR
VL - 34
IS - 3
SP - [289]
EP - 308
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 continuous time.
LA - eng
KW - maximum likelihood estimation; information divergence; Gaussian process; autoregressive processes; maximum likelihood estimation; information divergence; Gaussian process; autoregressive processes
UR - http://eudml.org/doc/33355
ER -

References

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  1. Anděl J., Statistical Analysis of Time Series (in Czech), SNTL, Prague 1976 
  2. Dzhaparidze K., Parameter Estimation and Hypothesis Testing in Spectral Analysis of Stationary Time Series, (Springer Series in Statistics.) Springer Verlag, Berlin 1986 Zbl0584.62157MR0812272
  3. Hájek J., On the simple linear model for Gaussian processes, In: Trans. of the 2nd Prague Conference, Academia, Prague 1959, pp. 185–197 (1959) 
  4. Hájek J., On linear statistical problems in stochastic processes, Czechoslovak Math. J. 12 (87) (1962), 404–444 (1962) MR0152090
  5. Michálek J., Asymptotic Rényi’s rate of Gaussian processes, Problems Control Inform. Theory 19 (1990), 3, 209–227 (1990) Zbl0705.62079
  6. Michálek J., Maximum likelihood principle and I -divergence: observations in discrete time, Kybernetika 34 (1998), 265–288 (1998) MR1640966
  7. Pisarenko V. F., On absolute continuity of the measures corresponding to a rational spectral density function (in Russian), Teor. Veroyatnost. i Primenen. IV (1959), 481–481 (1959) 
  8. Pisarenko V. F., On parameter estimations of a Gaussian stationary processes with a spectral density function (in Russian), Lithuanian Math. J. (1962) (1962) 
  9. Rozanov J. A., On application a central limit theorem, In: Proc. Fourth Berkeley Symp. Math. Stat. Prob., Berkeley 1961, Vol. 2 (1961) 

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