62 research outputs found
Some properties of the unified skew-normal distribution
For the family of multivariate probability distributions variously denoted as
unified skew-normal, closed skew-normal and other names, a number of properties
are already known, but many others are not, even some basic ones. The present
contribution aims at filling some of the missing gaps. Specifically, the
moments up to the fourth order are obtained, and from here the expressions of
the Mardia's measures of multivariate skewness and kurtosis. Other results
concern the property of log-concavity of the distribution, and closure with
respect to conditioning on intervals
Skewed Factor Models Using Selection Mechanisms
Traditional factor models explicitly or implicitly assume that the factors follow a multivariate normal distribution; that is, only moments up to order two are involved. However, it may happen in real data problems that the first two moments cannot explain the factors. Based on this motivation, here we devise three new skewed factor models, the skew-normal, the skew-t, and the generalized skew-normal factor models depending on a selection mechanism on the factors. The ECME algorithms are adopted to estimate related parameters for statistical inference. Monte Carlo simulations validate our new models and we demonstrate the need for skewed factor models using the classic open/closed book exam scores dataset
A note on the Fisher information matrix for the skew-generalized-normal model
In this paper, the exact form of the Fisher information matrix for the skew-generalized normal (SGN) distribution is determined. The existence of singularity problems of this matrix for the skew-normal and normal particular cases is investigated. Special attention is given to the asymptotic properties of the MLEs under the skew-normality hypothesis
On the non-identifiability of unified skew-normal distributions
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
Sub-dimensional Mardia measures of multivariate skewness and kurtosis
The Mardia measures of multivariate skewness and kurtosis summarize the
respective characteristics of a multivariate distribution with two numbers.
However, these measures do not reflect the sub-dimensional features of the
distribution. Consequently, testing procedures based on these measures may fail
to detect skewness or kurtosis present in a sub-dimension of the multivariate
distribution. We introduce sub-dimensional Mardia measures of multivariate
skewness and kurtosis, and investigate the information they convey about all
sub-dimensional distributions of some symmetric and skewed families of
multivariate distributions. The maxima of the sub-dimensional Mardia measures
of multivariate skewness and kurtosis are considered, as these reflect the
maximum skewness and kurtosis present in the distribution, and also allow us to
identify the sub-dimension bearing the highest skewness and kurtosis.
Asymptotic distributions of the vectors of sub-dimensional Mardia measures of
multivariate skewness and kurtosis are derived, based on which testing
procedures for the presence of skewness and of deviation from Gaussian kurtosis
are developed. The performances of these tests are compared with some existing
tests in the literature on simulated and real datasets
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