Parameter estimation for the supercritical contact process

Contact processes - and, more generally, interacting particle processes - can serve as models for a large variety of statistical problems, especially if we allow some simple modifications that do not essentially complicate the mathematical treatment of these processes. We begin a statistical study of the supercritical contact process that starts with a single infected site at the origin and is conditioned on survival of the infection. We consider the statistical problem of estimating the parameter

λ

of the process on the basis of an observation of the process at a single time

t.

We propose an estimator of

λ

and show that it is consistent and asymptotically normal as

t

→ ∞.