Open Access
August 2012 Skew-symmetric distributions and Fisher information – a tale of two densities
Marc Hallin, Christophe Ley
Bernoulli 18(3): 747-763 (August 2012). DOI: 10.3150/12-BEJ346

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.

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Marc Hallin. Christophe Ley. "Skew-symmetric distributions and Fisher information – a tale of two densities." Bernoulli 18 (3) 747 - 763, August 2012. https://doi.org/10.3150/12-BEJ346

Information

Published: August 2012
First available in Project Euclid: 28 June 2012

zbMATH: 1243.62068
MathSciNet: MR2948899
Digital Object Identifier: 10.3150/12-BEJ346

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

Rights: Copyright © 2012 Bernoulli Society for Mathematical Statistics and Probability

Vol.18 • No. 3 • August 2012
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