  We prove that kernel density estimation on symmetric spaces of non-compact
type, whose L2-risk was bounded above in previous work (Asta,2021), in fact
achieves a minimax rate of convergence. With this result, the story for kernel
density estimation on all symmetric spaces is completed. The idea in adapting
the proof for Euclidean space is to suitably abstract vector space operations
on Euclidean space to both actions of symmetric groups and reparametrizations
of Helgason-Fourier transforms and to use the fact that the exponential map for
symmetric spaces of non-compact type defines a diffeomorphism.
