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We construct a kernel density estimator on symmetric spaces of non-compacttype and establish an upper bound for its convergence rate, analogous to theminimax rate for classical kernel density estimators on Euclidean space.Symmetric spaces of non-compact type include hyperboloids of constant negativecurvature and spaces of symmetric positive definite matrices. This paperobtains a simplified formula in the special case when the symmetric space isthe space of normal distributions, a 2-dimensional hyperboloid.

Kernel Density Estimation on Symmetric Spaces of Non-Compact Type