Estimation of entropy for Poisson marked point processes

TL;DR

This paper introduces a kernel-based estimator for the differential entropy of marks in a Poisson marked point process, proving its consistency and asymptotic normality on a Riemannian manifold.

Contribution

It proposes a novel kernel estimator for entropy in Poisson marked point processes with continuous marks on Riemannian manifolds, and establishes its theoretical properties.

Findings

Estimator is $L^2$ consistent.

Estimator is almost surely consistent.

Asymptotic normality is proven.

Abstract

In this paper, a kernel estimator of the differential entropy of the mark distribution of a homogeneous Poisson marked point process is proposed. The marks have an absolutely continuous distribution on a compact Riemannian manifold without boundary. $L^2$ and almost surely consistency of this estimator as well as its asymptotic normality are investigated.