Kernel Density Estimation on Symmetric Spaces of Non-Compact Type

2014/11/14 by Dena Marie Asta, Asta, Dena Marie · 1 citation
Mathematics · Computer Science · #Statistical Methods and Inference #Bayesian Methods and Mixture Models

paper · pdf · doi:10.48550/arxiv.1411.4040

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 negative curvature 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.

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• Wishart kernel density estimation for strongly mixing time series on the cone of positive definite matrices

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