Kernel density estimation on symmetric spaces of non-compact type

JOURNAL OF MULTIVARIATE ANALYSIS

卷:181

Article

Asta, Dena Marie¹ 

[1] Ohio State Univ, Dept Stat, 1958 Neil Ave, Columbus, OH 43210 USA

关键词: Harmonic analysis;    Helgason-Fourier transform;    Kernel density estimator;    Non-Euclidean geometry;    Non-parametric;   

DOI  :  10.1016/j.jmva.2020.104676

来源: Elsevier

【 摘 要 】

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. (C) 2020 Elsevier Inc. All rights reserved.

【 授权许可】

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