On Generalized Sch\"urmann Entropy Estimators
Information Theory
2021-11-30 v1 Statistical Mechanics
math.IT
Data Analysis, Statistics and Probability
Abstract
We present a new class of estimators of Shannon entropy for severely undersampled discrete distributions. It is based on a generalization of an estimator proposed by T. Schuermann, which itself is a generalization of an estimator proposed by myself in arXiv:physics/0307138. For a special set of parameters they are completely free of bias and have a finite variance, something with is widely believed to be impossible. We present also detailed numerical tests where we compare them with other recent estimators and with exact results, and point out a clash with Bayesian estimators for mutual information.
Keywords
Cite
@article{arxiv.2111.11175,
title = {On Generalized Sch\"urmann Entropy Estimators},
author = {Peter Grassberger},
journal= {arXiv preprint arXiv:2111.11175},
year = {2021}
}
Comments
5 pages, 3 figures