Geodesic
Line metric for the entropy estimation
Modelirovanie i analiz informacionnyh sistem, Tome 16 (2009) no. 1, pp. 44-53

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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},
     publisher = {mathdoc},
     volume = {16},
     number = {1},
     year = {2009},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MAIS_2009_16_1_a3/}
}
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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/