Guyon, Xavier; Pumo, Besnik Space-time estimation of a particle system model. (Estimation spatio-temporelle d’un modèle de système de particules.) (French) Zbl 1061.62126 C. R., Math., Acad. Sci. Paris 340, No. 8, 619-622 (2005). Summary: Let \(X\) be a discrete time contact process (CP) on \(\mathbb Z^2\) as defined by R. Durrett and S. A. Levin [Phil. Trans. R. Soc. London, Ser. B 343, 329–350 (1994); see also SIAM Rev. 41, No. 4, 677–718 (1999; Zbl 0940.60086)]. We study the estimation of the model based on space-time evolution of \(X\), that is, \(T+1\) successive observations of \(X\) on a finite subset \(S\) of sites. We consider the maximum marginal pseudo-likelihood (MPL) estimator and show that, when \(T\to \infty\), this estimator is consistent and asymptotically normal for a non vanishing supercritical CP. Cited in 1 Document MSC: 62M09 Non-Markovian processes: estimation 62F12 Asymptotic properties of parametric estimators Citations:Zbl 0940.60086 PDFBibTeX XMLCite \textit{X. Guyon} and \textit{B. Pumo}, C. R., Math., Acad. Sci. Paris 340, No. 8, 619--622 (2005; Zbl 1061.62126) Full Text: DOI References: [1] Besag, J., Spatial interaction and the statistical analysis of lattice systems, J. Roy. Statist. Soc. Ser. B, 36, 192-225 (1974) · Zbl 0327.60067 [2] Dacunha-Castelle, D.; Duflo, M., Probability & Statistics, vol. 2 (1986), Springer: Springer Berlin [3] Durrett, R., Ten lectures on particle systems, (Cours de Saint Flour (1993). Cours de Saint Flour (1993), Lecture Notes in Math., vol. 1608 (1995), Springer: Springer Berlin), 97-201 · Zbl 0840.60088 [4] Durrett, R.; Levin, S. A., Stochastic spatial models: a user’s guide to ecological applications, Philos. Trans. Roy. Soc. London Ser. B, 343, 329-350 (1994) [5] Fiocco, M.; Zwet, W. R., Parameter estimation for the supercritical contact process, Bernoulli, 9, 1071-1092 (2003) · Zbl 1052.62087 [6] Guyon, X., Random Fields on a Network: Modelling, Statistics and Applications (1995), Springer: Springer Berlin [7] Hall, P.; Heyde, C. C., Martingale Limit Theory and its Application (1980), Academic Press · Zbl 0462.60045 [8] Jensen, J. L.; Künsch, H. R., On asymptotic normality of pseudo-likelihood estimate for pairwise interaction processes, Ann. Inst. Statist. Math., 46, 475-486 (1994) · Zbl 0820.62083 [9] Mollison, D., Spatial contact models for ecological and epidemic spread, with discussion, J. Roy. Statist. Soc. Ser. B, 39, 283-326 (1977) · Zbl 0374.60110 [10] Whittle, P., On stationary process in the plane, Biometrika, 41, 434-449 (1954) · Zbl 0058.35601 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.