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Skew-Symmetric Distributions and Fisher Information. The Double Sin of the Skew-Normal

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  • Marc Hallin
  • Christophe Ley

Abstract

Hallin and Ley (2012) investigate and fully characterize the Fisher singularity phenomenonin univariate and multivariate families of skew-symmetric distributions. Thispaper proposes a refined analysis of the (univariate) Fisher degeneracy problem, showingthat it can be more or less severe, inducing n1/4 (“simple singularity”), n1/6 (“doublesingularity”), or n1/8 (“triple singularity”) consistency rates for the skewness parameter.We show, however, that simple singularity (yielding n1/4 consistency rates),if any singularity at all, is the rule, in the sense that double and triple singularities arepossible for generalized skew-normal families only. We also show that higher-ordersingularities, leading to worse-than-n1/8 rates, cannot occur.

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Bibliographic Info

Paper provided by ULB -- Universite Libre de Bruxelles in its series Working Papers ECARES with number 2013/128686.

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Length: 20 p.
Date of creation: Sep 2012
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Publication status: Published by:
Handle: RePEc:eca:wpaper:2013/128686

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Keywords: Skewing function; Skew-Normal distributions;

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