Campbell equilibrium equation and pseudo-likelihood estimation for non-hereditary Gibbs point processes
David Dereudre and Frédéric Lavancier
Source: Bernoulli Volume 15, Number 4
(2009), 1368-1396.
Abstract
In this paper, we study Gibbs point processes involving a hardcore interaction which is not necessarily hereditary. We first extend the famous Campbell equilibrium equation, initially proposed by Nguyen and Zessin [Math. Nachr. 88 (1979) 105–115], to the non-hereditary setting and consequently introduce the new concept of removable points. A modified version of the pseudo-likelihood estimator is then proposed, which involves these removable points. We consider the following two-step estimation procedure: first estimate the hardcore parameter, then estimate the smooth interaction parameter by pseudo-likelihood, where the hardcore parameter estimator is plugged in. We prove the consistency of this procedure in both the hereditary and non-hereditary settings.
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Keywords: Campbell measure; consistency; Gibbs point process; non-hereditary interaction; pseudo-likelihood estimator; spatial statistics
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Permanent link to this document: http://projecteuclid.org/euclid.bj/1262962240
Digital Object Identifier: doi:10.3150/09-BEJ198
Zentralblatt MATH identifier: 1200.62023
Mathematical Reviews number (MathSciNet): MR2597597
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