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Selection of a Metric for the Nearest Neighbor Entropy Estimators

Abstract

We consider the problem of improving the efficiency of the nonparametric entropy estimation for a stationary ergodic process. Our approach is based on the nearest-neighbor distances. We propose a broad class of metrics on the space of right-sided infinite sequences drawn from a finite alphabet. The new metric has a parameter that is a nonincreasing function. We prove that, under certain conditions, our estimators have a small variance and show that a special selection of the metric parameters reduces the estimator’s bias.

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Correspondence to E. Timofeev.

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Translated from Fundamentalnaya i Prikladnaya Matematika, Vol. 18, No. 2, pp. 209–227, 2013.

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Timofeev, E. Selection of a Metric for the Nearest Neighbor Entropy Estimators. J Math Sci 203, 892–906 (2014). https://doi.org/10.1007/s10958-014-2181-8

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Keywords

  • Entropy
  • Auxiliary Parameter
  • Entropy Rate
  • Entropy Estimator
  • Markov Measure