Bias of the entropy estimator for symmetric Bernoulli measures and the weak metric
Modelirovanie i analiz informacionnyh sistem, Tome 19 (2012) no. 1, pp. 52-59.

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

We consider symmetric Bernoulli measures and new weak metrics and obtain a closed-form expression of the entropy estimator bias.
Keywords: entropy; nonparametric statistics; bias; Bernoulli measure.
@article{MAIS_2012_19_1_a3,
     author = {N. E. Timofeeva},
     title = {Bias of the  entropy estimator for symmetric {Bernoulli} measures and the weak metric},
     journal = {Modelirovanie i analiz informacionnyh sistem},
     pages = {52--59},
     publisher = {mathdoc},
     volume = {19},
     number = {1},
     year = {2012},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MAIS_2012_19_1_a3/}
}
TY  - JOUR
AU  - N. E. Timofeeva
TI  - Bias of the  entropy estimator for symmetric Bernoulli measures and the weak metric
JO  - Modelirovanie i analiz informacionnyh sistem
PY  - 2012
SP  - 52
EP  - 59
VL  - 19
IS  - 1
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/MAIS_2012_19_1_a3/
LA  - ru
ID  - MAIS_2012_19_1_a3
ER  - 
%0 Journal Article
%A N. E. Timofeeva
%T Bias of the  entropy estimator for symmetric Bernoulli measures and the weak metric
%J Modelirovanie i analiz informacionnyh sistem
%D 2012
%P 52-59
%V 19
%N 1
%I mathdoc
%U http://geodesic.mathdoc.fr/item/MAIS_2012_19_1_a3/
%G ru
%F MAIS_2012_19_1_a3
N. E. Timofeeva. Bias of the  entropy estimator for symmetric Bernoulli measures and the weak metric. Modelirovanie i analiz informacionnyh sistem, Tome 19 (2012) no. 1, pp. 52-59. http://geodesic.mathdoc.fr/item/MAIS_2012_19_1_a3/

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

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

[3] E. A. Timofeev, “Smeschenie neparametricheskoi otsenki entropii dlya markovskoi mery”, Zapiski nauchnykh seminarov POMI, 384, 2010, 267–290

[4] E. A. Timofeev, “Vybor metriki dlya neparametricheskikh otsenok entropii”, Matematika v Yaroslavskom universitete, sbornik obzornykh statei: k 35-letiyu matematicheskogo fakulteta, YarGU, Yaroslavl, 2011, 187–198

[5] G. Khardi, Raskhodyaschiesya ryady, IL, M., 1951

[6] M. Deza, E. Deza, Encyclopedia of Distances, Springer, 2009 | MR

[7] 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

[8] 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