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SUMMARY:Adaptive estimation of the copula correlation matrix for semiparam
 etic elliptical copulas - Marten H. Wegkamp\, Cornell University
DTSTART:20140625T090000Z
DTEND:20140625T093000Z
UID:TALK53112@talks.cam.ac.uk
CONTACT:37296
DESCRIPTION:In this joint work with Yue Zhao (Cornell University)\, we stu
 dy the adaptive estimation of copula correlation\nmatrix  for elliptical 
 copulas. In this context\, the correlations are connected to Kendalls tau 
 through a\nsine function transformation. Hence\, a natural estimate for  
 is the plug-in estimator b\nwith Kendalls tau\nstatistic. We rst obtain 
 a sharp bound for the operator norm of b\n􀀀 . Then\, we study a facto
 r model for\n\, for which we propose a rened estimator e\nby tting a l
 ow-rank matrix plus a diagonal matrix to b\nusing\nleast squares with a n
 uclear norm penalty on the low-rank matrix. The bound on the operator norm
  b\n􀀀 \nserves to scale the penalty term\, and we obtain nite sample
  oracle inequalities for e. We also consider an\nelementary factor model 
 of \, for which we propose closed-form estimators. We provide data-driven
  versions\nfor all our estimation procedures and performance bounds.
LOCATION:Centre for Mathematical Sciences\, Meeting Room 2
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