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SUMMARY:Tail index estimation\, concentration\, adaptation... - Stéphane 
 Boucheron (Paris Diderot)
DTSTART:20160520T150000Z
DTEND:20160520T160000Z
UID:TALK65796@talks.cam.ac.uk
CONTACT:Quentin Berthet
DESCRIPTION:This paper presents an adaptive version of the Hill estimator 
 based on Lespki's model selection method. This simple data-driven index se
 lection method is shown to satisfy an oracle inequality and is checked to 
 achieve the lower bound recently derived by Carpentier and Kim. In order t
 o establish the oracle inequality\, we derive non-asymptotic variance boun
 ds and concentration inequalities for Hill estimators. These concentration
  inequalities are derived from Talagrand's concentration inequality for sm
 ooth functions of independent exponentially distributed random variables c
 ombined with three tools of Extreme Value Theory: the quantile transform\,
  Karamata's representation of slowly varying functions\, and Rényi's char
 acterisation for the order statistics of exponential samples. The performa
 nce of this computationally and conceptually simple method is illustrated 
 using Monte-Carlo simulations.
LOCATION:MR12\, Centre for Mathematical Sciences\, Wilberforce Road\, Camb
 ridge.
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