On the non-identifiability of unified skew-normal distributions

04/20/2023

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by   Kesen Wang, et al.

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In this note, 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 parametrizations and extends to the family of unified skew-elliptical distributions and more generally to selection distibutions. We provide several suggestions to make the unified skew-normal model identifiable and describe various sub-models that are identifiable.