Minimum kolmogorov distance estimates for multivariate parametrized families

American Journal of Mathematical and Management Sciences

Volumn 16, Issue 1-2, 1996, Pages 167-191

  Gyorfi L ^a,b,c   Vajda, I ^a,b,c   Van der Meulen, E ^a,b,c  

^a BUDAPEST UNIVERSITY OF TECHNOLOGY AND ECONOMICS   (Hungary)

^b INSTITUTE OF MATHEMATICS   (Czech Republic)

^c UNIVERSITY OF LEUVEN   (Belgium)

Author keywords

Consistency; Consistency in the L1 norm; Kolmogorov distance; Minimum distance density estimates; Minimum distance point estimates; Multivariate models; Rate of consistency

Indexed keywords

MATHEMATICAL MODELS; PARAMETER ESTIMATION; STATISTICAL METHODS;

CONSISTENCY RATE; KOLMOGOROV DISTANCE PARAMETER ESTIMATES; MULTIVARIATE MODELS;

PROBABILITY DENSITY FUNCTION;

EID: 0030379705     PISSN: 01966324     EISSN: None     Source Type: Journal    
DOI: 10.1080/01966324.1996.10737415     Document Type: Article

References (11)

1. Devroye L. P., (1977): A uniform bound for the deviation of empirical distribution functions. J. Multivar. Analysis 7, 594-597.
2. Devroye L., Gyorfi L. (1985): Nonparametric Density Estimation: The View. Wiley, New York.
3. Gyorfi L., Vajda I., van der Meulen E. (1994a): Parameter estimation by projecting on structural statistical models. Proc. 5th Prague Conf. on Asympt. Statist. (Ed. by P. Mandl, M. Huskova), Physica Verlag, Wien, 261-272.
4. Gyorfi L., Vajda I., van der Meulen E. (1994b): Minimum Hellinger distance point estimates consistent under weak family regularity. Mathem. Methods of Statistics 3, 25-45.
5. Gyorfi L., Vajda I., van der Meulen E. (1995): Minimum Kolmogorov distance estimates of parameters and parametrized distributions. Metrika 42.
6. Huber P. J. (1981): Robust Statistics. Wiley, New York.
7. Ibragimov I. A., Hasminskii R. Z. (1981): Statistical Estimation, Asymptotic Theory. Springer, Berlin 1981.
8. Kiefer J. (1961): On large deviations of the empiric d.f. of vector chance variables and a law of iterated logarithm. Pacific J. Math. 11, 649-660.
9. Landers D., Rogge L. (1972): Characterization of the topologies used in the theory of maximum likelihood estimation. Zeitschr. Wahrsch. Verw. Geb. 21, 197-200.
10. Vajda I. (1969): On the convergence of information contained in a sequence of observations. Proc. of Colloquium on Inform. Theory in Debrecen (Hungary), 1967. Bolyai Math. Soc., Budapest, 489-501.
11. Vajda I. (1989): Theory of Statistical Inference and Information. Kluwer, Boston.