Best asymptotic normality of the kernel density entropy estimator for smooth densities

IEEE Transactions on Information Theory

Volumn 45, Issue 4, 1999, Pages 1321-1326

  Eggermont, Paul P B ^a   Lariccia, Vincent N ^a  

^a UNIVERSITY OF DELAWARE   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

PROBABILITY DENSITY FUNCTION; RANDOM PROCESSES;

ENTROPY ESTIMATION; KERNEL DENSITY ESTIMATORS; KULLBACK-LEIBLER DIVERGENCE;

INFORMATION THEORY;

EID: 0032690752     PISSN: 00189448     EISSN: None     Source Type: Journal    
DOI: 10.1109/18.761291     Document Type: Article

References (21)

1. I. A. Ahmad and P. E. Lin A nonparametric estimation of the entropy for absolutely continuous distributions," IEEE Trans Inform. Theory, vol. 36, pp. 688692, 1989.
2. A. R. Barron, L. Györfi, and E. C. van der Meulen Distribution estimation consistent in total variation and in two types of information divergence," IEEE Trans Inform. Theory, vol. 38, pp. 14371454, 1992.
3. J. Beirlant, E. Dudewicz, L. Gyorfi, and E. G. van der Meulen Nonparametric entropy estimation: An overview," Int. J Math Stat Sei., vol. 6, pp. 1739, 1997.
4. L. Breiman, Probability. Reading, MA: AddisonWesley, 1968.
5. L. Devroye, A Course in Density Estimation. Boston, MA: Birkhäuser, 1987.
6. L. Devroye and L. Györfi, Nonparametric Density Estimation. New York: Wiley, 1985.
7. P. P. B. Eggermont and V. N. LaRiccia Maximum smoothed likelihood density estimation," J Nonparam. Statist., vol. 4, pp. 211222, 1995.
8. _ Nonlinearly smoothed EM density estimation with automatic smoothing parameter selection for nonparametric deconvolution problems," J Amer. Statist. Assoc., vol. 97 pp. 14511458, 1997.
9. _ Optimal convergence rates for Good's nonparametric maximum likelihood density estimator," unpublished manuscript, Jan. 1998.
10. I. J. Good and R. A. Gaskins Nonparametric roughness penalties for probability densities," Biometrika, vol. 58, pp. 255277, 1971.
11. L. Györfi and E. C. van der Meulen Densityfree convergence properties of various estimators of the entropy," Comput. Statist. Data Anal., vol. 5, pp. 425436, 1987.
12. _ An entropy estimate based on a kernel density estimation," Colloq. Math. Soc. J. Botyai, no. 57: Limit Theorems in Probability and Statistics, I. Berkes, E. Csâki, P. Révçsz, Eds. Amsterdam, The Netherlands: NorthHolland, 1990.
13. P. Hall On powerful distributional tests based on sample spacings," J. Multivar. Statist., vol. 19, pp. 201225, 1986.
14. _ On KullbackLeibler loss and density estimation," Ann. Statist., vol. 14, pp. 14911495, 1987.
15. P. Hall and S. C. Morton On the estimation of entropy," Ann. Inst. Statist. Math., vol. 45, pp. 6988, 1993.
16. H. Joe Estimation of entropy and other functional of a multivariate density," Ann. Inst. Statist. Math., vol. 41, pp. 683697, 1989.
17. B. Ya. Levit Asymptotically efficient estimation of nonlinear functionals," Probl. Inform. Transm., vol. 14, pp. 204209, 1978.
18. A. Mokkadem Estimation of entropy and information of absolutely continuous random variables," IEEE Trans Inform. Theory, vol. 35, pp. 193196, 1989.
19. J. R. Thompson and R. A. Tapia, Nonparametric Function Estimation, Modeling, and Simulation. Philadelphia, PA: SIAM, 1990.
20. A. B. Tsybakov and E. C. van der Meulen Root n consistent estimators of entropy for densities with unbounded support," Scand. J. Statist., vol. 23, pp. 7583, 1994.
21. B. van Es Estimating functionals related to a density by a class of statistics based on spacings," Scand. J. Statist., vol. 19, pp. 6172, 1992.