  In this paper, we observe a sparse mean vector through Gaussian noise and we
aim at estimating some additive functional of the mean in the minimax sense.
More precisely, we generalize the results of (Collier et al., 2017, 2019) to a
very large class of functionals. The optimal minimax rate is shown to depend on
the polynomial approximation rate of the marginal functional, and optimal
estimators achieving this rate are built.
