On the non-identifiability of unified skew-normal distributions

2023/04/20 by Wang, Kesen, Arellano-Valle, Reinaldo B., Azzalini, Adelchi +1 · 1 citation
#FOS: Mathematics #Probability (math.PR) #Statistics Theory (math.ST)

paper · doi:10.48550/arxiv.2304.10445

Abstract

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.

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