Bernoulli

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  • Volume 15, Number 4 (2009), 1368-1396.

Campbell equilibrium equation and pseudo-likelihood estimation for non-hereditary Gibbs point processes

David Dereudre and Frédéric Lavancier

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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.

Article information

Source
Bernoulli, Volume 15, Number 4 (2009), 1368-1396.

Dates
First available in Project Euclid: 8 January 2010

Permanent link to this document
https://projecteuclid.org/euclid.bj/1262962240

Digital Object Identifier
doi:10.3150/09-BEJ198

Mathematical Reviews number (MathSciNet)
MR2597597

Zentralblatt MATH identifier
1200.62023

Keywords
Campbell measure consistency Gibbs point process non-hereditary interaction pseudo-likelihood estimator spatial statistics

Citation

Dereudre, David; Lavancier, Frédéric. Campbell equilibrium equation and pseudo-likelihood estimation for non-hereditary Gibbs point processes. Bernoulli 15 (2009), no. 4, 1368--1396. doi:10.3150/09-BEJ198. https://projecteuclid.org/euclid.bj/1262962240


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