  We study the problem of parameter estimation for large exchangeable
interacting particle systems when a sample of discrete observations from a
single particle is known. We propose a novel method based on martingale
estimating functions constructed by employing the eigenvalues and
eigenfunctions of the generator of the mean field limit, where the law of the
process is replaced by the (unique) invariant measure of the mean field
dynamics. We then prove that our estimator is asymptotically unbiased and
asymptotically normal when the number of observations and the number of
particles tend to infinity, and we provide a rate of convergence towards the
exact value of the parameters. Finally, we present several numerical
experiments which show the accuracy of our estimator and corroborate our
theoretical findings, even in the case the mean field dynamics exhibit more
than one steady states.
