Authors: | Hallin, Marc Ley, Christophe |
Title: | Skew-symmetric distributions and Fisher information |
Other Titles: | The double sin of the skew-normal |
Language (ISO): | en |
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. |
Subject Headings: | Consistency rates Singular Fisher information Skewing function Skew-normal distributions Skew-symmetric distributions Symmetric kernel |
URI: | http://hdl.handle.net/2003/29644 http://dx.doi.org/10.17877/DE290R-10367 |
Issue Date: | 2012-09-26 |
Appears in Collections: | Sonderforschungsbereich (SFB) 823 |
Files in This Item:
File | Description | Size | Format | |
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DP_3712_SFB823_Hallin_Ley.pdf | DNB | 222.41 kB | Adobe PDF | View/Open |
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