Previous |  Up |  Next


maximum likelihood estimate; information divergence; exponential families; discrete time process; autoregressive sequences
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.
[1] Anderson T. W.: The Statistical Analysis of Time Series. Wiley, New York 1971 MR 0283939 | Zbl 0835.62074
[2] Basseville M., Benveniste A.: Detection of Abrupt Changes in Signals and Dynamical Systems. Springer–Verlag, Berlin 1986 Zbl 0578.93056
[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
[4] Kullback S.: Information Theory and Statistics (in Russian). Nauka, Moscow 1967. Translated from the English original
[5] Kupperman M.: Further application of information theory to multivariate analysis and statistical inference. Ann. Math. Statist. 27 (1956), 1184
[6] Kűchler V., Sorensen M.: Exponential families of stochastic processes: A unifying semimartingale approach. Internat. Statist. Rev. (1989), 123–144 DOI 10.2307/1403382
[7] Michálek J.: Yule–Walker estimates and asymptotic $I$-divergence rate. Problems Control Inform. Theory 19 (1990), 5–6, 387–398 MR 1086831 | Zbl 0744.62126
[8] Michálek J.: A method of detecting changes in the behaviour of locally stationary sequences. Kybernetika 31 (1995), 1, 17–29 MR 1324658 | Zbl 0868.62070
[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
[10] Page E.: Continuous inspection schemes. Biometrika 41 (1954), 100–115 DOI 10.1093/biomet/41.1-2.100 | MR 0088850 | Zbl 0056.38002
Partner of
EuDML logo