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Estimating the reduced moments of a random measure

Part of: Geometric probability and stochastic geometry Inference from stochastic processes Stochastic processes

Published online by Cambridge University Press:  01 July 2016

Kiên Kiêu  and
Marianne Mora
Kiên Kiêu*
Affiliation:
INRA, France
Marianne Mora*
Affiliation:
Université Paris-X
*
∗ Postal address: Unité de Biométrie, INRA, route de Saint-Cyr, F78026 Versailles Cedex, France. Email address: kieu@versailles.inra.fr
∗∗ Postal address: U.F.R. de sciences économiques, Université Paris-X, 200 avenue de la république, 92001 Nanterre Cedex, France.
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Abstract

We consider a random measure for which distribution is invariant under the action of a standard transformation group. The reduced moments are defined by applying classical theorems on invariant measure decomposition. We present a general method for constructing unbiased estimators of reduced moments. Several asymptotic results are established under an extension of the Brillinger mixing condition. Examples related to stochastic geometry are given.

Keywords

Brillinger mixing conditionedge effectmoment measurenon-parametric estimationpalm distributionpoint processstochastic geometryunbiased estimation

MSC classification

Primary: 60G57: Random measures
Secondary: 60D05: Geometric probability and stochastic geometry 62M99: None of the above, but in this section
Type
Stochastic Geometry and Statistical Applications
Information
Advances in Applied Probability , Volume 31 , Issue 1 , March 1999 , pp. 48 - 62
Copyright
Copyright © Applied Probability Trust 1999 

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