On the non-identifiability of unified skew-normal distributions
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Date
2023
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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.
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Keywords
latent variable, non-identifiability, permutation, selection distribution, unified skew-elliptical distribution, unified skew-normal distribution