Skew-symmetric distributions and Fisher information: A tale of two densities

M. Hallin, C. Ley

    Research output: Contribution to journalArticleScientificpeer-review

    26 Citations (Scopus)

    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.
    Original languageEnglish
    Pages (from-to)747-763
    JournalBernoulli
    Volume18
    Issue number3
    Publication statusPublished - 2012

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