Geodesic
On asymptotics of the entropy estimator bias for~Bernoulli~measures
Modelirovanie i analiz informacionnyh sistem, Tome 16 (2009) no. 4, pp. 96-108.

Voir la notice de l'article provenant de la source Math-Net.Ru

We consider Bernoulli measures and obtain a closed-form expression of the entropy estimator bias.
Keywords: entropy, nonparametric statistic, Bernoulli measure.
Mots-clés : moments 
@article{MAIS_2009_16_4_a8,
     author = {E. A. Timofeev},
     title = {On asymptotics of the entropy estimator bias {for~Bernoulli~measures}},
     journal = {Modelirovanie i analiz informacionnyh sistem},
     pages = {96--108},
     publisher = {mathdoc},
     volume = {16},
     number = {4},
     year = {2009},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MAIS_2009_16_4_a8/}
}
TY  - JOUR
AU  - E. A. Timofeev
TI  - On asymptotics of the entropy estimator bias for~Bernoulli~measures
JO  - Modelirovanie i analiz informacionnyh sistem
PY  - 2009
SP  - 96
EP  - 108
VL  - 16
IS  - 4
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/MAIS_2009_16_4_a8/
LA  - ru
ID  - MAIS_2009_16_4_a8
ER  - 
%0 Journal Article
%A E. A. Timofeev
%T On asymptotics of the entropy estimator bias for~Bernoulli~measures
%J Modelirovanie i analiz informacionnyh sistem
%D 2009
%P 96-108
%V 16
%N 4
%I mathdoc
%U http://geodesic.mathdoc.fr/item/MAIS_2009_16_4_a8/
%G ru
%F MAIS_2009_16_4_a8
E. A. Timofeev. On asymptotics of the entropy estimator bias for~Bernoulli~measures. Modelirovanie i analiz informacionnyh sistem, Tome 16 (2009) no. 4, pp. 96-108. http://geodesic.mathdoc.fr/item/MAIS_2009_16_4_a8/

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

[2] P. Flajolet, R. Sedgewick, Analytic Combinatorics, Cambridge University Press, 2008 | MR | Zbl

[3] 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

[4] A. Kaltchenko, N. Timofeeva, “Rate of convergence of the nearest neighbor entropy estimator”, AEU - International Journal of Electronics and Communications, 64:1 (2010), 75–79 | DOI

[5] D. Knut, Iskusstvo programmirovaniya dlya EVM, v. 3, Mir, M., 1978 | MR

[6] D. Martin, Dzh. Inglend, Matematicheskaya teoriya entropii, Mir, M., 1988 | MR | Zbl

[7] Wojtek Szpankowski, Average Case Analysis of Algorithms on Sequences, John Wiley Sons, New York, 2001 | MR

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