On the non-identifiability of unified skew-normal distributions

Kesen Wang; Reinaldo B. Arellano-Valle; Adelchi Azzalini; Marc G. Genton

doi:10.1002/sta4.597

On the non-identifiability of unified skew-normal distributions

Kesen Wang, Reinaldo B. Arellano-Valle, Adelchi Azzalini, Marc G. Genton

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Abstract

We investigate the non-identifiability of the multivariate unified skew-normal distribution under permutation of its latent variables. We show that the non-identifiability issue also holds with other parameterizations and extends to the family of unified skew-elliptical distributions and more generally to selection distributions. We provide several suggestions to make the unified skew-normal model identifiable and describe various sub-models that are identifiable.

Original language	English (US)
Journal	Stat
Volume	12
Issue number	1
DOIs	https://doi.org/10.1002/sta4.597
State	Published - Jul 17 2023

Bibliographical note

KAUST Repository Item: Exported on 2023-07-28
Acknowledgements: The research of Kesen Wang and Marc G. Genton was supported by the King Abdullah University of Science and Technology (KAUST).

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10.1002/sta4.597

https://repository.kaust.edu.sa/bitstream/10754/692550/5/2304.10445.pdf

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N2 - We investigate the non-identifiability of the multivariate unified skew-normal distribution under permutation of its latent variables. We show that the non-identifiability issue also holds with other parameterizations and extends to the family of unified skew-elliptical distributions and more generally to selection distributions. We provide several suggestions to make the unified skew-normal model identifiable and describe various sub-models that are identifiable.

AB - We investigate the non-identifiability of the multivariate unified skew-normal distribution under permutation of its latent variables. We show that the non-identifiability issue also holds with other parameterizations and extends to the family of unified skew-elliptical distributions and more generally to selection distributions. We provide several suggestions to make the unified skew-normal model identifiable and describe various sub-models that are identifiable.

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On the non-identifiability of unified skew-normal distributions

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