Open Access
2024 A new parameterization for elliptically symmetric angular Gaussian distributions of arbitrary dimension
Zehao Yu, Xianzheng Huang
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Electron. J. Statist. 18(1): 301-334 (2024). DOI: 10.1214/23-EJS2210


We consider a class of angular Gaussian distributions that allows different degrees of isotropy for directional random variables of arbitrary dimension. To incorporate constraints imposed on the original model parameters, we propose a new parameterization of the distribution so that all new model parameters are free of constraints. Via the new parameterization, we translate the original problem of maximum likelihood estimation subject to complex constraints to a routine optimization problem free of constraints, which in turn leads to theoretically sound and numerically stable procedures for drawing likelihood-based inference. Byproducts from the likelihood-based inference are used to develop graphical and numerical diagnostic tools for assessing goodness of fit of this distribution in a data application. Simulation study and application to data from a hydrogeology study are used to demonstrate implementation and performance of the inference procedures and diagnostics methods.


We are grateful to the two anonymous referees for their detailed suggestions and thought-provoking comments on earlier versions this manuscript. Their suggestions greatly improved the manuscript, and their comments inspired new ideas for our follow-up research.


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Zehao Yu. Xianzheng Huang. "A new parameterization for elliptically symmetric angular Gaussian distributions of arbitrary dimension." Electron. J. Statist. 18 (1) 301 - 334, 2024.


Received: 1 July 2022; Published: 2024
First available in Project Euclid: 1 February 2024

Digital Object Identifier: 10.1214/23-EJS2210

Keywords: Angular Gaussian distribution , Compositional data , maximum likelihood , residual

Vol.18 • No. 1 • 2024
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