Mardia, K. V., Kent, J. T. orcid.org/0000-0002-1861-8349 and Laha, A. K. (2016) Score matching estimators for directional distributions. [Preprint - arXiv]
Abstract
One of the major problems for maximum likelihood estimation in the well-established directional models is that the normalising constants can be difficult to evaluate. A new general method of "score matching estimation" is presented here on a compact oriented Riemannian manifold. Important applications include von Mises-Fisher, Bingham and joint models on the sphere and related spaces. The estimator is consistent and asymptotically normally distributed under mild regularity conditions. Further, it is easy to compute as a solution of a linear set of equations and requires no knowledge of the normalizing constant. Several examples are given, both analytic and numerical, to demonstrate its good performance.
Metadata
Item Type: | Preprint |
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Authors/Creators: |
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Dates: |
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Institution: | The University of Leeds |
Academic Units: | The University of Leeds > Faculty of Engineering & Physical Sciences (Leeds) > School of Mathematics (Leeds) > Statistics (Leeds) |
Depositing User: | Symplectic Publications |
Date Deposited: | 14 Oct 2024 09:24 |
Last Modified: | 14 Oct 2024 09:24 |
Published Version: | https://arxiv.org/abs/1604.08470 |
Identification Number: | 10.48550/arXiv.1604.08470 |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:123205 |