Browsing by Author "Wang, Kesen"

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    Multivariate unified skew-t distributions and their properties
    (2024) Wang, Kesen; Karling, Maicon J.; Arellano-Valle, Reinaldo B.; Genton, Marc G.
    The unified skew-t (SUT) is a flexible parametric multivariate distribution that accounts for skewness and heavy tails in the data. A few of its properties can be found scattered in the literature or in a parameterization that does not follow the original one for unified skew- normal (SUN) distributions, yet a systematic study is lacking. In this work, explicit properties of the multivariate SUT distribution are presented, such as its stochastic representations, moments, SUN-scale mixture representation, linear transformation, additivity, marginal distribution, canonical form, quadratic form, conditional distribution, change of latent dimensions, Mardia measures of multivariate skewness and kurtosis, and non-identifiability issue. These results are given in a parameterization that reduces to the original SUN distribution as a sub- model, hence facilitating the use of the SUT for applications. Several models based on the SUT distribution are provided for illustration.
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    On the non-identifiability of unified skew-normal distributions
    (2023) Wang, Kesen; Arellano-Valle, Reinaldo B.; Azzalini, Adelchi; Genton, Marc G.
    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.