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Kernel density estimation on symmetric spaces of non-compact type

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  • Asta, Dena Marie

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.

Suggested Citation

  • Asta, Dena Marie, 2021. "Kernel density estimation on symmetric spaces of non-compact type," Journal of Multivariate Analysis, Elsevier, vol. 181(C).
    • Handle: RePEc:eee:jmvana:v:181:y:2021:i:c:s0047259x20302578
    DOI: 10.1016/j.jmva.2020.104676
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    References listed on IDEAS

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    1. Pelletier, Bruno, 2005. "Kernel density estimation on Riemannian manifolds," Statistics & Probability Letters, Elsevier, vol. 73(3), pages 297-304, July.
    2. Kim, Yoon Tae & Park, Hyun Suk, 2013. "Geometric structures arising from kernel density estimation on Riemannian manifolds," Journal of Multivariate Analysis, Elsevier, vol. 114(C), pages 112-126.
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    Cited by:

    1. Ouimet, Frédéric, 2022. "A symmetric matrix-variate normal local approximation for the Wishart distribution and some applications," Journal of Multivariate Analysis, Elsevier, vol. 189(C).
    2. Yuewei Wang & Hang Chen & Xinyang Wu, 2021. "Spatial Structure Characteristics of Tourist Attraction Cooperation Networks in the Yangtze River Delta Based on Tourism Flow," Sustainability, MDPI, vol. 13(21), pages 1-16, October.

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