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This paper investigates the estimation of the interaction function for aclass of McKean-Vlasov stochastic differential equations. The estimation isbased on observations of the associated particle system at time $T$,considering the scenario where both the time horizon $T$ and the number ofparticles $N$ tend to infinity. Our proposed method recovers polynomial ratesof convergence for the resulting estimator. This is achieved under theassumption of exponentially decaying tails for the interaction function.Additionally, we conduct a thorough analysis of the transform of the associatedinvariant density as a complex function, providing essential insights for ourmain results.

Polynomial rates via deconvolution for nonparametric estimation in McKean-Vlasov SDEs