On the non‐identifiability of unified skew‐normal distributions

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.