  We observe the actions of a $K$ sub-sample of $N$ individuals up to time $t$
for some large $K\le N$. We model the relationships of individuals by i.i.d.
Bernoulli($p$)-random variables, where $p\in (0,1]$ is an unknown parameter.
The rate of action of each individual depends on some unknown parameter $\mu>
0$ and on the sum of some function $\phi$ of the ages of the actions of the
individuals which influence him. The parameters $\mu$ and $\phi$ are considered
as nuisance parameters. The aim of this paper is to obtain a central limit
theorem for the estimator of $p$ that we introduced in \cite{D}, both in the
subcritical and supercritical cases.
