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arXiv · 1801.02050

Statistical estimation of the Shannon entropy

Alexander Bulinski·Denis Dimitrov
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Abstract

The behavior of the Kozachenko - Leonenko estimates for the (differential) Shannon entropy is studied when the number of i.i.d. vector-valued observations tends to infinity. The asymptotic unbiasedness and L^2-consistency of the estimates are established. The conditions employed involve the analogues of the Hardy - Littlewood maximal function. It is shown that the results are valid in particular for the entropy estimation of any nondegenerate Gaussian vector.

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Alexander Bulinski, Denis Dimitrov. 2018-01-06. Statistical estimation of the Shannon entropy. https://arxiv.org/abs/1801.02050

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