  We study the problem of learning unknown parameters in stochastic interacting
particle systems with polynomial drift, interaction and diffusion functions
from the path of one single particle in the system. Our estimator is obtained
by solving a linear system which is constructed by imposing appropriate
conditions on the moments of the invariant distribution of the mean field limit
and on the quadratic variation of the process. Our approach is easy to
implement as it only requires the approximation of the moments via the ergodic
theorem and the solution of a low-dimensional linear system. Moreover, we prove
that our estimator is asymptotically unbiased in the limits of infinite data
and infinite number of particles (mean field limit). In addition, we present
several numerical experiments that validate the theoretical analysis and show
the effectiveness of our methodology to accurately infer parameters in systems
of interacting particles.
