Bernoulli

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  • Volume 18, Number 3 (2012), 747-763.

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

Marc Hallin and Christophe Ley

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Abstract

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.

Article information

Source
Bernoulli, Volume 18, Number 3 (2012), 747-763.

Dates
First available in Project Euclid: 28 June 2012

Permanent link to this document
https://projecteuclid.org/euclid.bj/1340887000

Digital Object Identifier
doi:10.3150/12-BEJ346

Mathematical Reviews number (MathSciNet)
MR2948899

Zentralblatt MATH identifier
1243.62068

Keywords
singular Fisher information skew-normal distributions skew-symmetric distributions skewing function symmetric kernel

Citation

Hallin, Marc; Ley, Christophe. Skew-symmetric distributions and Fisher information – a tale of two densities. Bernoulli 18 (2012), no. 3, 747--763. doi:10.3150/12-BEJ346. https://projecteuclid.org/euclid.bj/1340887000


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