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

By Marc Hallin, Christophe Ley. 2012

56 citations recorded by the source corpus.

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.

Subfields: Finance, Statistical and Nonlinear Physics, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/7df06c15075853354672b4c21575e5d37239b2c9

Citations in the corpus

• On Families of Distributions with Shape Parameters (2015, unknown): “But even in Family 1, the problem only occurs for some choices of g and w , depending on their relationship: see Hallin & Ley (2012) for a complete analysis of this (and for earlier references; the univariate case appears to be fully solved in their Section 2).”