On asymptotically optimal estimates for general observations

Stochastic Processes and their Applications

Volumn 72, Issue 1, 1997, Pages 27-45

  Vajda, Igor ^a   Janžura, Martin ^a  

^a INSTITUTE OF INFORMATION THEORY AND AUTOMATION   (Czech Republic)

Author keywords

Diffusion processes; Generalized M estimators; Markov Gibbs random fields; Maximum likelihood estimators

Indexed keywords

EID: 0031520667     PISSN: 03044149     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0304-4149(97)00082-3     Document Type: Article

References (19)

1. Brown, L.D., 1986. Fundamentals of statistical exponential families. Lecture Notes, vol. 9, Inst. of Math. Statist. Hayward, CA.
2. Chapman D.G., Robbins, H.E., 1951. Minimum variance estimation without regularity assumptions. Ann. Math. Statist. 22, 581-586.
3. Comets, F., 1992. On consistency of a class of estimators for exponential families of Markov random fields on a lattice. Ann. Statist. 20, 455-468.
4. Drygas, H., 1976. Weak and strong consistency of the least squares estimators in regression models. Z. Wahrsch. verw. Gebiete 34, 119-127.
5. Ellis, R.S., 1985. Entropy, Large Deviations, and Statistical Mechanics. Springer, Berlin.
6. Georgii, H.-O., 1988. Gibbs Measures and Phase Transitions. DeGruyter, Berlin.
7. Haberman, S.J., 1989. Concavity and estimation. Ann. Statist. 17, 1631-1661.
8. Huber, P.J., 1981. Robust Statistics: A Review, Wiley, New York.
9. Janžura, M., 1997. Asymptotic results in parameter estimation for Gibbs random fields. Kybernetika 33, 133-159.
10. Küchler, U., Sørensen, M., 1989. Exponential families of stochastic processes: A unifying semimartingale approach. Internat. Statist. Rev. 57, 123-144.
11. Liese, F., Vajda, I., 1994. Consistency of M-estimates in general regression models. J. Multivariate Anal. 50, 93-114.
12. Liese, F., Vajda, I., 1995. Necessary and sufficient conditions for consistency of generalized M-estimates. Metrika 42, 291-324.
13. Luschgy, H., 1993. Second order behavior of Neyman-Pearson tests for stochastic processes. Statist. Decisions 11, 133-150.
14. Niemiro, W., 1992. Asymptotics for M-estimators defined by convex minimization. Ann. Statist. 20 (3), 1514-1533.
15. Rockefellar, R.T., 1970. Convex Analysis, Princeton University Press, Princeton, NJ.
16. Strasser, H., 1981. Consistency of maximum likelihood and Bayes estimates. Ann. Statist. 9, 1107-1113.
17. Vajda, I., 1994. Conditions equivalent and doubly equivalent to consistency of approximate MLE's. J. Italian Statist. Soc. 2, 107-125.
18. Vajda, I., 1995. Conditions equivalent to consistency of approximate MLE's for stochastic processes. Stochastic Process and Appl. 56, 35-56.
19. Younès, L., 1989. Parametric inference for imperfectly observed Gibbsian fields. Probab. Theory Related Fields 82, 625-645.