Estimating the reduced moments of a random measure
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Advances in Applied Probability

Estimating the reduced moments of a random measure

Kiên Kiêu and Marianne Mora

Source: Adv. in Appl. Probab. Volume 31, Number 1 (1999), 48-62.

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.

Primary Subjects: 60G57
Secondary Subjects: 60D05, 62M99
Keywords: Brillinger mixing condition; edge effect; moment measure; non-parametric estimation; palm distribution; point process; stochastic geometry; unbiased estimation

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Links and Identifiers

Permanent link to this document: http://projecteuclid.org/euclid.aap/1029954265
Digital Object Identifier: doi:10.1239/aap/1029954265
Mathematical Reviews number (MathSciNet): MR1699660
Zentralblatt MATH identifier: 0926.62093


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