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.

翻译：本文研究了多元统一偏正态分布在其潜变量排列下的非可识别性问题。我们证明，该非可识别性问题在其它参数化形式下同样存在，并且扩展至统一偏椭圆分布族及更一般的选择分布。我们提出了若干使统一偏正态模型可识别的建议，并描述了多种具有可识别性的子模型。