Statistical estimation of the Shannon entropy
Statistics Theory
2018-01-09 v1 Statistics Theory
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.
Keywords
Cite
@article{arxiv.1801.02050,
title = {Statistical estimation of the Shannon entropy},
author = {Alexander Bulinski and Denis Dimitrov},
journal= {arXiv preprint arXiv:1801.02050},
year = {2018}
}