Skew-symmetric distributions and Fisher information — a tale of two densities

Skew-symmetric densities recently received much attention in the literature, giving rise to increasingly general families of univariate and multivariate skewed densities. Most of those families, however, suffer from the inferential drawback of a potentially singular Fisher information in the vicinit...

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Bibliographic Details
Published in:Bernoulli : official journal of the Bernoulli Society for Mathematical Statistics and Probability 2012-08, Vol.18 (3), p.747-763
Main Authors: HALLIN, MARC, LEY, CHRISTOPHE
Format: Article
Language:English
Subjects:
Covariance matrices
Degrees of freedom
Fisher information
Gaussian distributions
Information economics
Mathematical functions
Mathematical independent variables
Matrices
singular Fisher information
skew-normal distributions
skew-symmetric distributions
Skewed distribution
skewing function
Standardization
symmetric kernel
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Summary:Skew-symmetric densities recently received much attention in the literature, giving rise to increasingly general families of univariate and multivariate skewed densities. Most of those families, however, suffer from the inferential drawback of a potentially singular Fisher information in the vicinity of symmetry. All existing results indicate that Gaussian densities (possibly after restriction to some linear subspace) play a special and somewhat intriguing role in that context. We dispel that widespread opinion by providing a full characterization, in a general multivariate context, of the information singularity phenomenon, highlighting its relation to a possible link between symmetric kernels and skewing functions - a link that can be interpreted as the mismatch of two densities.
ISSN:1350-7265
DOI:10.3150/12-bej346