Statistics for the contact process

Marta Fiocco and Willem R. Van Zwet

Statistica Neerlandica, 2002, vol. 56, issue 2, 243-251

Abstract: A d‐dimensional contact process is a simplified model for the spread of an infection on the lattice Zd. At any given time t≥0, certain sites x∈Zd are infected while the remaining once are healthy. Infected sites recover at constant rate 1, while healthy sites are infected at a rate proportional to the number of infected neighboring sites. The model is parametrized by the proportionality constant λ. If λ is sufficiently small, infection dies out (subcritical process), whereas if λ is sufficiently large infection tends to be permanent (supercritical process). In this paper we study the estimation problem for the parameter λ of the supercritical contact process starting with a single infected site at the origin. Based on an observation of this process at a single time t, we obtain an estimator for the parameter λ which is consistent and asymptotically normal as t→∞

Date: 2002
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