| Title:
|
Maximum likelihood principle and $I$-divergence: continuous time observations (English) |
| Author:
|
Michálek, Jiří |
| Language:
|
English |
| Journal:
|
Kybernetika |
| ISSN:
|
0023-5954 |
| Volume:
|
34 |
| Issue:
|
3 |
| Year:
|
1998 |
| Pages:
|
[289]-308 |
| 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 continuous time. (English) |
| Keyword:
|
maximum likelihood estimation |
| Keyword:
|
information divergence |
| Keyword:
|
Gaussian process |
| Keyword:
|
autoregressive processes |
| MSC:
|
62B10 |
| MSC:
|
62F10 |
| MSC:
|
62F12 |
| MSC:
|
62M10 |
| idZBL:
|
Zbl 1274.62067 |
| idMR:
|
MR1640970 |
| . |
| Date available:
|
2009-09-24T19:16:16Z |
| Last updated:
|
2015-03-28 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/135208 |
| . |
| Related article:
|
http://dml.cz/handle/10338.dmlcz/135207 |
| . |
| Reference:
|
[1] Anděl J.: Statistical Analysis of Time Series (in Czech).SNTL, Prague 1976 |
| Reference:
|
[2] Dzhaparidze K.: Parameter Estimation and Hypothesis Testing in Spectral Analysis of Stationary Time Series.(Springer Series in Statistics.) Springer Verlag, Berlin 1986 Zbl 0584.62157, MR 0812272 |
| Reference:
|
[3] Hájek J.: On the simple linear model for Gaussian processes.In: Trans. of the 2nd Prague Conference, Academia, Prague 1959, pp. 185–197 |
| Reference:
|
[4] Hájek J.: On linear statistical problems in stochastic processes.Czechoslovak Math. J. 12 (87) (1962), 404–444 MR 0152090 |
| Reference:
|
[5] Michálek J.: Asymptotic Rényi’s rate of Gaussian processes.Problems Control Inform. Theory 19 (1990), 3, 209–227 Zbl 0705.62079 |
| Reference:
|
[6] Michálek J.: Maximum likelihood principle and $I$-divergence: observations in discrete time.Kybernetika 34 (1998), 265–288 MR 1640966 |
| Reference:
|
[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 |
| Reference:
|
[8] Pisarenko V. F.: On parameter estimations of a Gaussian stationary processes with a spectral density function (in Russian).Lithuanian Math. J. (1962) |
| Reference:
|
[9] Rozanov J. A.: On application a central limit theorem.In: Proc. Fourth Berkeley Symp. Math. Stat. Prob., Berkeley 1961, Vol. 2 |
| . |
