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Saddlepoint approximations for the normalizing constant of Fisher-Bingham distributions on products of spheres and Stiefel manifolds

Kume, Alfred, Preston, S. P., Wood, Andrew T.A. (2013) Saddlepoint approximations for the normalizing constant of Fisher-Bingham distributions on products of spheres and Stiefel manifolds. Biometrika, 100 (4). pp. 971-984. ISSN 1464-3510. (doi:10.1093/biomet/ast021) (The full text of this publication is not currently available from this repository. You may be able to access a copy if URLs are provided)

The full text of this publication is not currently available from this repository. You may be able to access a copy if URLs are provided. (Contact us about this Publication)
Official URL
http://dx.doi.org/10.1093/biomet/ast021

Abstract

In an earlier paper Kume & Wood (2005) showed how the normalizing constant of the Fisher–Bingham distribution on a sphere can be approximated with high accuracy using a univariate saddlepoint density approximation. In this sequel, we extend the approach to a more general setting and derive saddlepoint approximations for the normalizing constants of multicomponent Fisher–Bingham distributions on Cartesian products of spheres, and Fisher–Bingham distributions on Stiefel manifolds. In each case, the approximation for the normalizing constant is essentially a multivariate saddlepoint density approximation for the joint distribution of a set of quadratic forms in normal variables. Both first-order and second-order saddlepoint approximations are considered. Computational algorithms, numerical results and theoretical properties of the approximations are presented. In the challenging high-dimensional settings considered in this paper the saddlepoint approximations perform very well in all examples considered.

Item Type: Article
DOI/Identification number: 10.1093/biomet/ast021
Additional information: number of additional authors: 2; article number: n/a;
Uncontrolled keywords: Directional data, Fisher matrix distribution, Kent distribution
Subjects: Q Science > QA Mathematics (inc Computing science)
Divisions: Faculties > Sciences > School of Mathematics Statistics and Actuarial Science
Depositing User: Stewart Brownrigg
Date Deposited: 07 Mar 2014 00:05 UTC
Last Modified: 20 Feb 2020 04:05 UTC
Resource URI: https://kar.kent.ac.uk/id/eprint/40466 (The current URI for this page, for reference purposes)
Kume, Alfred: https://orcid.org/0000-0001-7683-1693
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