Geodesic
Line metric for the entropy estimation
Modelirovanie i analiz informacionnyh sistem, Tome 16 (2009) no. 1, pp. 44-53 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

The problem of the estimation of the entropy of a stationary process $\mu$ is considered. A new metric is constructed for the nonparametric entropy estimator. It is shown that the estimator converges almost surely and its variance is upper-bounded by $\mathcal O(n^{-1})$ for a large class of stationary ergodic processes with a finite state space. For the class of the symmetric Bernoulli measures an explicit formula for the estimator bias is obtained.
Mots-clés : estimation
Keywords: entropy, stationary process, metric, nonparametric estimator, symmetric Bernoulli measure. 
@article{MAIS_2009_16_1_a3,
     author = {N. E. Timofeeva},
     title = {Line metric for the entropy estimation},
     journal = {Modelirovanie i analiz informacionnyh sistem},
     pages = {44--53},
     year = {2009},
     volume = {16},
     number = {1},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MAIS_2009_16_1_a3/}
}
TY  - JOUR
AU  - N. E. Timofeeva
TI  - Line metric for the entropy estimation
JO  - Modelirovanie i analiz informacionnyh sistem
PY  - 2009
SP  - 44
EP  - 53
VL  - 16
IS  - 1
UR  - http://geodesic.mathdoc.fr/item/MAIS_2009_16_1_a3/
LA  - ru
ID  - MAIS_2009_16_1_a3
ER  - 
%0 Journal Article
%A N. E. Timofeeva
%T Line metric for the entropy estimation
%J Modelirovanie i analiz informacionnyh sistem
%D 2009
%P 44-53
%V 16
%N 1
%U http://geodesic.mathdoc.fr/item/MAIS_2009_16_1_a3/
%G ru
%F MAIS_2009_16_1_a3
N. E. Timofeeva. Line metric for the entropy estimation. Modelirovanie i analiz informacionnyh sistem, Tome 16 (2009) no. 1, pp. 44-53. http://geodesic.mathdoc.fr/item/MAIS_2009_16_1_a3/

[1] I. S. Gradshtein , I. M. Ryzhik, Tablitsy integralov, summ, ryadov i proizvedenii, Nauka, M., 1971

[2] L. Devroye, “Exponentional inequalities in nonpametric estimation”, Nonparametric Functional Estimation and Related Topics, NATO ASI Series, ed. G. Roussas, Kluwer Academic Publishers, Dordrecht, 1991, 31–44 | MR

[3] C. McDiarmid, “On the method of bounded differences”, Surveys in Combinatorics, Cambridge University Press, Cambridge, 1989, 148–188 | MR

[4] A. Kaltchenko, N. Timofeeva, “Entropy Estimators with Almost Sure Convergence and an $O(n^{-1})$ Variance”, Advances in Mathematics of Communications, 2:1 (2008), 1–13 | DOI | MR | Zbl

[5] A. Kaltchenko, N. Timofeeva, “Rate of convergence of the nearest neighbor entropy estimator”, Int. J. Electron. Commun. (AEU), 62:12 (2008) | MR

[6] E. A. Timofeev, “Statisticheski otsenivaemye invarianty mer”, Algebra i analiz, 17:3 (2005), 204–236 | MR