A general definition of symmetry for a directional model is given. Then the information matrix for the parameters indexing a symmetric density is shown to be block-diagonal: one block for the location and one block for the shape. This result is used to construct an algorithm for the efficient estimation of the parameters. Examples are given; a new symmetric distribution, the $FB_6$ is introduced; it generalizes the classical distributions on the hypersphere.
Publié le : 1984-09-14
Classification:
Bingham distribution,
Fisher distribution,
maximum likelihood estimation,
von Mises distribution,
62F12,
62E20
@article{1176346724,
author = {Rivest, Louis-Paul},
title = {On the Information Matrix for Symmetric Distributions on the Hypersphere},
journal = {Ann. Statist.},
volume = {12},
number = {1},
year = {1984},
pages = { 1085-1089},
language = {en},
url = {http://dml.mathdoc.fr/item/1176346724}
}
Rivest, Louis-Paul. On the Information Matrix for Symmetric Distributions on the Hypersphere. Ann. Statist., Tome 12 (1984) no. 1, pp. 1085-1089. http://gdmltest.u-ga.fr/item/1176346724/