SFB 823 Skew - symmetric distributions and Fisher information The double sin of the skew - normal
نویسندگان
چکیده
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 n (“simple singularity”), n (“double singularity”), or n (“triple singularity”) consistency rates for the skewness parameter. We show, however, that simple singularity (yielding n 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-n rates, cannot occur.
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