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

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

2007-09-12

arxiv.org/abs/0709.1801v4

Bernoulli 2009, Vol. 15, No. 4, 1368-1396

Mathematics

Statistics Theory

Published in at http://dx.doi.org/10.3150/09-BEJ198 the Bernoulli (http://isi.cbs.nl/bernoulli/) by the International Statisti

Scientific paper

10.3150/09-BEJ198

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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