Space-time estimation of a particle system model

Xavier Guyon (1, 2) , Besnik Pumo (3)

1 SAMOS - Statistique Appliquée et MOdélisation Stochastique
2 CES - Centre d'économie de la Sorbonne
3 INHP - Institut National d'Horticulture et du Paysage

Let X be a discrete time contact process (CP) on the discrete bidimensional lattice as define by Durett - Levin (1994) . We study estimation of the model based on space-time evolution on a finite subset of sites. For this, we make use of a marginal pseudo-likelihood. The estimator obtained is consistent and asymptoticaly normal for non-vanishing supercritical CP. Numerical studies confirm these results.

Mots clés: Contact process; parameter estimation; supercritical process; sub-ergodicity; marginal pseudo-likelihood; triangular martingale array.; triangular martingale array

Domaines: Statistiques [math.ST]; Théorie [stat.TH]

Xavier Guyon, Besnik Pumo. Space-time estimation of a particle system model. Statistics A Journal of Theoretical and Applied Statistics, 2007, 41 (5), pp.395-407. ⟨10.1080/02331880701399074⟩. ⟨hal-00256589⟩