Ralf Hielscher: Kernel Density Estimation on the Rotation Group

Author(s):

Ralf Hielscher

Title:

Kernel Density Estimation on the Rotation Group

Electronic source:

application/pdf

Preprint series:

Technische Universität Chemnitz, Fakultät für Mathematik (Germany). Preprint 7, 2010

Mathematics Subject Classification:

62G07	[]
43A75	[]

Abstract: We are concerned with kernel density estimation on the rotation group SO(3) and the corresponding mean integrated squared error. We give lower and upper bounds for different function classes and derive optimal kernel functions. Furthermore, we consider approximations to the mean integrated squared error that depend on certain Sobolev norms of the density function and analyze them with respect to asymptotic behavior and optimal kernel functions. We compare our optimal kernels functions to families of kernel functions commonly used for kernel density estimation on the rotation group. Finally, we give a fast algorithm for the computation of the kernel density estimator for large sampling sets and verify our theoretical findings by numerical experiments.

Keywords:

kernel density estimation, rotation group, harmonic analysis

Language:

English

Publication time:

06/2010