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Estimation of entropy for Poisson marked point processes

Part of:Stochastic processesLimit theoremsInference from 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: patricia.alonso-ruiz@uconn.edu
** Postal address: Ulm University, Helmholtzstr. 18, 89081 Ulm, Germany. Email address: evgeny.spodarev@uni-ulm.de
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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 L 2 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 fields60F05: Central limit and other weak theorems

Information

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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