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 Model. Anal. Inform. Sist., 2009, Volume 16, Number 1, Pages 44–53 (Mi mais47)

Line metric for the entropy estimation

N. E. Timofeeva

P. G. Demidov Yaroslavl State University

Abstract: 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.

Keywords: estimation, entropy, stationary process, metric, nonparametric estimator, symmetric Bernoulli measure

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UDC: 517.51

Citation: N. E. Timofeeva, “Line metric for the entropy estimation”, Model. Anal. Inform. Sist., 16:1 (2009), 44–53

Citation in format AMSBIB
\Bibitem{Tim09} \by N.~E.~Timofeeva \paper Line metric for the entropy estimation \jour Model. Anal. Inform. Sist. \yr 2009 \vol 16 \issue 1 \pages 44--53 \mathnet{http://mi.mathnet.ru/mais47}