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On the exact maximum likelihood inference of Fisher–Bingham distributions using an adjusted holonomic gradient method

Kume, Alfred, Sei, Tomonari (2017) On the exact maximum likelihood inference of Fisher–Bingham distributions using an adjusted holonomic gradient method. Statistics and Computing, 28 . ISSN 0960-3174. E-ISSN 1573-1375. (doi:10.1007/s11222-017-9765-3) (KAR id:63200)

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http://dx.doi.org/10.1007%2Fs11222-017-9765-3

Abstract

Holonomic function theory has been successfully implemented in a series of recent papers to efficiently calculate the normalizing constant and perform likelihood estimation for the Fisher–Bingham distributions. A key ingredient for establishing the standard holonomic gradient algorithms is the calculation of the Pfaffian equations. So far, these papers either calculate these symbolically or apply certain methods to simplify this process. Here we show the explicit form of the Pfaffian equations using the expressions from Laplace inversion methods. This improves on the implementation of the holonomic algorithms for these problems and enables their adjustments for the degenerate cases. As a result, an exact and more dimensionally efficient ODE is implemented for likelihood inference.

Item Type: Article
DOI/Identification number: 10.1007/s11222-017-9765-3
Uncontrolled keywords: Bingham distributions, Fisher–Bingham distributions, Directional statistics, Holonomic functions
Subjects: Q Science
Q Science > QA Mathematics (inc Computing science)
Divisions: Faculties > Sciences > School of Mathematics Statistics and Actuarial Science
Depositing User: Alfred Kume
Date Deposited: 04 Sep 2017 09:07 UTC
Last Modified: 20 Feb 2020 04:09 UTC
Resource URI: https://kar.kent.ac.uk/id/eprint/63200 (The current URI for this page, for reference purposes)
Kume, Alfred: https://orcid.org/0000-0001-7683-1693
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