  This paper concerns the nonparametric estimation problem of the
distribution-state dependent drift vector field in an interacting $N$-particle
system. Observing single-trajectory data for each particle, we derive the
mean-field rate of convergence for the maximum likelihood estimator (MLE),
which depends on both Gaussian complexity and Rademacher complexity of the
function class. In particular, when the function class contains $\alpha$-smooth
H{\"o}lder functions, our rate of convergence is minimax optimal on the order
of $N^{-\frac{\alpha}{d+2\alpha}}$. Combining with a Fourier analytical
deconvolution argument, we derive the consistency of MLE for the external force
and interaction kernel in the McKean-Vlasov equation.
