Lower bounds for density estimation on symmetric spaces

Dena Marie Asta

Statistics & Probability Letters, 2025, vol. 223, issue C

Abstract: 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.

Keywords: Harmonic analysis; Helgason–Fourier transform; Kernel density estimator; Non-Euclidean geometry; Non-parametric (search for similar items in EconPapers)
Date: 2025
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DOI: 10.1016/j.spl.2025.110416

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