Kernel density estimation on symmetric spaces of non-compact type. (English) Zbl 1461.62245
Summary: We construct a kernel density estimator on symmetric spaces of non-compact type and establish an upper bound for its convergence rate, analogous to the minimax rate for classical kernel density estimators on Euclidean space. Symmetric spaces of non-compact type include hyperboloids of constant curvature \(- 1\) and spaces of symmetric positive definite matrices. This paper obtains a simplified formula in the special case when the symmetric space is the space of normal distributions, a 2-dimensional hyperboloid.
MSC:
| 62R40 | Topological data analysis |
| 62G07 | Density estimation |
| 43-04 | Software, source code, etc. for problems pertaining to abstract harmonic analysis |
Keywords:
harmonic analysis; Helgason-Fourier transform; kernel density estimator; non-Euclidean geometry; nonparametricReferences:
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