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
Issue Date: 2012-09-26
Appears in Collections:Sonderforschungsbereich (SFB) 823

Files in This Item:
File Description SizeFormat 
DP_3712_SFB823_Hallin_Ley.pdfDNB222.41 kBAdobe PDFView/Open

This item is protected by original copyright

Items in Eldorado are protected by copyright, with all rights reserved, unless otherwise indicated.