On the information matrix for symmetric distributions on the hypersphere
type: Item
instance of: scholarly article
title: On the information matrix for symmetric distributions on the hypersphere
zbMATH Open document ID: 0545.62035
author: Louis-Paul Rivest
published in: The Annals of Statistics
publication date: 1984-01-01T00:00:00Z
review text: In this work a general definition of symmetry for a directional model is given in terms of the invariance of the distribution with respect to a subgroup of O(k), the group of orthogonal transformations in \(R^ k\). 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.
Mathematics Subject Classification ID: 62H05
Mathematics Subject Classification ID: 62F12
Mathematics Subject Classification ID: 62E20
Mathematics Subject Classification ID: 62A01
zbMATH DE Number: 3868435
zbMATH Keywords: symmetric distributions on the hypersphere
zbMATH Keywords: Bingham distribution
zbMATH Keywords: Fisher distribution
zbMATH Keywords: maximum likelihood estimation
zbMATH Keywords: von Mises distribution
zbMATH Keywords: general definition of symmetry
zbMATH Keywords: directional model
zbMATH Keywords: group of orthogonal transformations
zbMATH Keywords: information matrix
zbMATH Keywords: block-diagonal
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1214/aos/1176346724
OpenAlex ID: W2080847705
DOI: 10.1214/AOS/1176346724
description: scientific article; zbMATH DE number 3868435