We introduce a novel kernel density estimator for a large class of symmetric spaces and prove a minimax rate of convergence as fast as the minimax rate on Euclidean space. We prove a minimax rate of convergence proven without any compactness assumptions on the space or Hölder-class assumptions on the densities. A main tool used in proving the convergence rate is the Helgason-Fourier transform, a generalization of the Fourier transform for semisimple Lie groups modulo maximal compact subgroups. This paper obtains a simplified formula in the special case when the symmetric space is the 2-dimensional hyperboloid.
CITATION STYLE
Asta, D. M. (2015). Kernel density estimation on symmetric spaces. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 9389, pp. 779–787). Springer Verlag. https://doi.org/10.1007/978-3-319-25040-3_83
Mendeley helps you to discover research relevant for your work.