Density-free convergence properties of various estimators of entropy
Let \(f(x)\) be a probability density function, \(x\in\mathbb R^d\). The Shannon (or differential) entropy is defined as \[ H(f)=-\int f(x)\log f(x)\,dx. \] In this paper we propose, based on a random sample \(X_1,\dots,X_n\) generated from \(f\), two new nonparametric estimators for \(H(f)\). Both entropy estimators are histogram-based in the sense that they involve a histogram-based density estimator \(\hat f_n\). We prove their a.s. consistency with the only condition on \(f\) that \(H(f)\) is finite.
scientific article; zbMATH DE number 4028627
scientific article