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Estimation of entropy for Poisson marked point processes

Part of: Inference from stochastic processes Limit theorems Stochastic processes

Published online by Cambridge University Press:  17 March 2017

P. Alonso-Ruiz  and
E. Spodarev
P. Alonso-Ruiz*
Affiliation:
Ulm University
E. Spodarev*
Affiliation:
Ulm University
*
* Current address: Department of Mathematics, University of Connecticut, 341 Mansfield Road, Unit 1009, Storrs, CT 06269-1009, USA. Email address: [email protected]
** Postal address: Ulm University, Helmholtzstr. 18, 89081 Ulm, Germany. Email address: [email protected]
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Abstract

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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. We investigate L2 and the almost surely consistency of this estimator as well as its asymptotic normality.

Keywords

Marked point processkernel density estimatorentropycentral limit theoremBoolean model

MSC classification

Primary: 62M30: Spatial processes
Secondary: 60G60: Random fields 60F05: Central limit and other weak theorems
Type
Research Article
Information
Advances in Applied Probability , Volume 49 , Issue 1 , March 2017 , pp. 258 - 278
Copyright
Copyright © Applied Probability Trust 2017 

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