Geodesic
Global information in statistical experiments and consistency of likelihood-based estimates and tests
Kybernetika, Tome 34 (1998) no. 3, pp. 245-263
Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

Voir la notice de l'article

In the framework of standard model of asymptotic statistics we introduce a global information in the statistical experiment about the occurrence of the true parameter in a given set. Basic properties of this information are established, including relations to the Kullback and Fisher information. Its applicability in point estimation and testing statistical hypotheses is demonstrated.
In the framework of standard model of asymptotic statistics we introduce a global information in the statistical experiment about the occurrence of the true parameter in a given set. Basic properties of this information are established, including relations to the Kullback and Fisher information. Its applicability in point estimation and testing statistical hypotheses is demonstrated.
Classification : 62B10, 62B15, 62F03, 62F10, 62F12
Keywords: information divergence; point estimation; testing statistical hypotheses 
@article{KYB_1998_34_3_a0,
     author = {Vajda, Igor},
     title = {Global information in statistical experiments and consistency of likelihood-based estimates and tests},
     journal = {Kybernetika},
     pages = {245--263},
     year = {1998},
     volume = {34},
     number = {3},
     mrnumber = {1640962},
     zbl = {1274.62069},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/KYB_1998_34_3_a0/}
}
TY  - JOUR
AU  - Vajda, Igor
TI  - Global information in statistical experiments and consistency of likelihood-based estimates and tests
JO  - Kybernetika
PY  - 1998
SP  - 245
EP  - 263
VL  - 34
IS  - 3
UR  - http://geodesic.mathdoc.fr/item/KYB_1998_34_3_a0/
LA  - en
ID  - KYB_1998_34_3_a0
ER  - 
%0 Journal Article
%A Vajda, Igor
%T Global information in statistical experiments and consistency of likelihood-based estimates and tests
%J Kybernetika
%D 1998
%P 245-263
%V 34
%N 3
%U http://geodesic.mathdoc.fr/item/KYB_1998_34_3_a0/
%G en
%F KYB_1998_34_3_a0
Vajda, Igor. Global information in statistical experiments and consistency of likelihood-based estimates and tests. Kybernetika, Tome 34 (1998) no. 3, pp. 245-263. http://geodesic.mathdoc.fr/item/KYB_1998_34_3_a0/

[1] Bahadur R. R.: Some Limit Theorems in Statistics. SIAM, Philadelphia 1971 | MR | Zbl

[2] Berk R. H.: Limiting behavior of posterior distributions when the model is incorrect. Ann. Math. Statist. 37 (1966), 51–58 | DOI | MR | Zbl

[3] Cover T. M., Thomas J. B.: Elements of Information Theory. Wiley, New York 1991 | MR | Zbl

[4] Groot, M H. De: Uncertainty, information and sequential experiments. Ann. Math. Statist. 33 (1962), 404–419 | DOI | MR

[5] Groot M. H. De: Optimal Statistical Decisions. McGraw Hill, New York 1970 | MR

[6] Gallager R. C.: Information Theory and Reliable Communication. Wiley, New York 1968 | Zbl

[7] Huber P. J.: Robust Statistics. Wiley, New York 1981 | MR

[8] Kullback S.: Information Theory and Statistics. Wiley, New York 1959 | MR | Zbl

[9] Lehman E. L.: Testing Statistical Hypotheses. Second edition. Wiley, New York 1986

[10] Liese F., Vajda I.: Necessary and sufficient conditions for consistency of generalized $M$-estimates. Metrika 42 (1995), 93–114 | DOI | Zbl

[11] Lindley D. V.: On the measure of the information provided by an experiment. Ann. Math. Statist. 27 (1956), 986–1005 | DOI

[12] Loéve M.: Probability Theory. Wiley, New York 1963

[13] Perlman M. D.: On the strong consistency of approximate maximum likelihood estimators. In: Proc. VIth Berkeley Symp. Prob. Math. Statist., 1972, pp. 263–281

[14] Pfanzagl J.: On the measurability and consistency of minimum contrast estimators. Metrika 14 (1969), 249–272 | DOI

[15] Pfanzagl J.: Parametric Statistical Theory. Walter de Guyter, Berlin 1994 | Zbl

[16] Rao C. R.: Linear Statistical Inference and its Applications. Wiley, New York 1965 | Zbl

[17] A: Rényi: On the amount of information concerning an unknown parameter in a sequence of observations. Publ. Math. Inst. Hungar. Acad. Sci., Sec. A 9 (1964), 617–625

[18] Rényi A.: Statistics and information theory. Stud. Scient. Math. Hungar. 2 (1967), 249–256 | Zbl

[19] Rockafellar R. T.: Convex Analysis. Princeton Univ. Press, Princeton, N. J. 1970

[20] Strasser H.: Consistency of maximum likelihood and Bayes estimates. Ann. Statist. 9 (1981), 1107–1113 | DOI | Zbl

[21] Strasser A.: Mathematical Theory of Statistics. DeGruyter, Berlin 1985 | Zbl

[22] Torgersen E.: Comparison of Statistical Experiments. Cambridge Univ. Press, Cambridge 1991 | Zbl

[23] Vajda I.: Conditions equivalent to consistency of approximate MLE’s for stochastic processes. Stochastic Process. Appl. 56 (1995), 35–56 | DOI | Zbl