Estimation of entropy for Poisson marked point processes

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.

24 pages, revised version, to appear in Advances in Applied probability 49.1

References in corpus (1)

• Normal approximation under local dependence