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SUMMARY:The Double Sin of the Skew-Normal: Skew-Symmetric Families of Dist
 ributions and Fisher Information - Marc Hallin\, Université libre de Brux
 elles
DTSTART:20140221T160000Z
DTEND:20140221T170000Z
UID:TALK50325@talks.cam.ac.uk
CONTACT:20082
DESCRIPTION:Families of skew-symmetric distributions (Azzalini 1985)  are 
 subject to  Fisher information singularity problems under symmetry. We  in
 vestigate this  phenomenon\, showing that it can be more or less severe\, 
 inducing n^1/4 ^ ("simple singularity")\, n^1/6 ^ ("double singularity")\,
   or n^1/8 ^ ("triple singularity") consistency rates for the skewness par
 ameter. We show\, however\, that  simple singularity (yielding n^1/4 ^ con
 sistency rates)\, if any singularity at all\, is the rule\, in the sense t
 hat double and triple singularities are possible for generalized skew-norm
 al families only.  We also show that higher-order singularities\, leading 
 to worse-than-n^1/8 ^ rates\, cannot occur.  A general reparametrization m
 ethod is suggested\, which applies in all models where Fisher information 
 misbehaves.\n\nBased on joint work with Christophe Ley
LOCATION:MR12\,  Centre for Mathematical Sciences\, Wilberforce Road\, Cam
 bridge
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