Kernel density estimation on symmetric spaces of non-compact type

Dena Marie Asta

Journal of Multivariate Analysis, 2021, vol. 181, issue C

Abstract: 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.

Keywords: Harmonic analysis; Helgason–Fourier transform; Kernel density estimator; Non-Euclidean geometry; Non-parametric (search for similar items in EconPapers)
Date: 2021
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Citations: View citations in EconPapers (2)

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DOI: 10.1016/j.jmva.2020.104676

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