This paper proposes a consistent nonparametric empirical Bayes estimator of the prior density for directional data. The methodology is to use Fourier analysis on $S^2$ to adapt Euclidean techniques to this non-Euclidean environment. General consistency results are obtained. In addition, a discussion of efficient numerical computation of Fourier transforms on $S^2$ is given, and their applications to the methods suggested in this paper are
sketched.
Publié le : 1996-02-14
Classification:
Consistency,
fast Fourier transform,
Legendre transform,
spherical harmonics,
62G05,
58G25
@article{1033066208,
author = {Healy, Dennis M. and Kim, Peter T.},
title = {An empirical Bayes approach to directional data and efficient computation on the sphere},
journal = {Ann. Statist.},
volume = {24},
number = {6},
year = {1996},
pages = { 232-254},
language = {en},
url = {http://dml.mathdoc.fr/item/1033066208}
}
Healy, Dennis M.; Kim, Peter T. An empirical Bayes approach to directional data and efficient computation on the sphere. Ann. Statist., Tome 24 (1996) no. 6, pp. 232-254. http://gdmltest.u-ga.fr/item/1033066208/