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.
Citation
David Dereudre. Frédéric Lavancier. "Campbell equilibrium equation and pseudo-likelihood estimation for non-hereditary Gibbs point processes." Bernoulli 15 (4) 1368 - 1396, November 2009. https://doi.org/10.3150/09-BEJ198
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