Skew-symmetric distributions and Fisher information
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Date
2012-09-26
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Abstract
Hallin and Ley (2012) investigate and fully characterize the Fisher singularity phenomenon in univariate and multivariate families of skew-symmetric distributions. This paper proposes a refined analysis of the (univariate) Fisher degeneracy problem, showing that it can be more or less severe, inducing n1/4 (“simple singularity”), n1/6 (“double singularity”), 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 are possible for generalized skew-normal families only. We also show that higher-order
singularities, leading to worse-than-n1/8 rates, cannot occur.
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Keywords
Consistency rates, Singular Fisher information, Skewing function, Skew-normal distributions, Skew-symmetric distributions, Symmetric kernel