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

Dereudre, David; Lavancier, Frédéric

Bernoulli, Tome 15 (2009) no. 1, p. 1368-1396 / Harvested from Project Euclid

Résumé

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.

Publié le : 2009-11-15
Classification: Campbell measure, consistency, Gibbs point process, non-hereditary interaction, pseudo-likelihood estimator, spatial statistics

@article{1262962240,
     author = {Dereudre, David and Lavancier, Fr\'ed\'eric},
     title = {Campbell equilibrium equation and pseudo-likelihood estimation for non-hereditary Gibbs point processes},
     journal = {Bernoulli},
     volume = {15},
     number = {1},
     year = {2009},
     pages = { 1368-1396},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1262962240}
}

Dereudre, David; Lavancier, Frédéric. Campbell equilibrium equation and pseudo-likelihood estimation for non-hereditary Gibbs point processes. Bernoulli, Tome 15 (2009) no. 1, pp.  1368-1396. http://gdmltest.u-ga.fr/item/1262962240/