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Locally asymptotic normality of Gibbs models on a lattice

Published online by Cambridge University Press:  01 July 2016

Shigeru Mase
Shigeru Mase*
Affiliation:
Hiroshima University
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Abstract

We consider the statistical estimation problem of potential functions of Gibbs models on the plane lattice. We assume that the area on which a random point pattern is observed is sufficiently large and take an asymptotic point of view. The main result is to show the locally asymptotic normality of the Gibbs model under certain conditions. From this result we can show the optimality of the maximum likelihood estimator employing known results about locally asymptotic normal families, though a practical computation of the maximum likelihood estimator presents difficulties. An estimation procedure based on the method of moments is also proposed.

Keywords

PLANE LATTICEASYMPTOTIC THEORYPOTENTIAL FUNCTIONMAXIMUM LIKELIHOOD ESTIMATORMOMENT ESTIMATOR
Type
Research Article
Information
Advances in Applied Probability , Volume 16 , Issue 3 , September 1984 , pp. 585 - 602
Copyright
Copyright © Applied Probability Trust 1984 

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Footnotes

This research was supported in part by a Grant-in-Aid for Scientific Research of the Ministry of Education, Science and Culture under Contract Number 321-6061-56530009.

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