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SUMMARY:Simultaneous confidences bands with the volume-of-tube formula and
  spline estimators - Tatyana Krivobokova (Goettingen)
DTSTART:20110527T133000Z
DTEND:20110527T143000Z
UID:TALK30798@talks.cam.ac.uk
CONTACT:Richard Nickl
DESCRIPTION:Simultaneous confidence bands for a smooth curve are typically
  based on\nlimit theorems for the supremum of standardized deviation of th
 e true\nfunction from its nonparametric estimator and related Gaussian\npr
 ocesses.\nHowever\, the convergence of suprema of Gaussian processes to th
 e\nlimiting\nextreme value distribution is exceedingly slow\, so that in f
 inite\nsamples\nsome bootstrap approximations need to be used\, which is r
 ather\ncomputationally intensive. Moreover\, in practice the unknown bias 
 and\nthe\nlarge variability of an estimated smoothing parameter complicate
  the\nmatter\nfurther.\nAlternatively\, one can consider a two-term approx
 imation to the tail\nprobability of suprema of Gaussian processes (Sun\, 1
 993)\, which turned\nout\nto be connected to the volume of a tube around a
  manifold embedded in a\nunit\nsphere. This approximation is much more acc
 urate and requires no\nbootstrap\neven in small samples. In this talk we c
 onsider simultaneous confidence\nbands based on the volume-of-tube formula
  for a smooth curve estimated\nwith\npenalized splines. In particular\, we
  discuss how the unknown bias and\nthe\nvariability of an estimated smooth
 ing parameter can be handled using the\n(empirical) Bayesian formulation o
 f spline estimators. This is the joint\nwork with Thomas Kneib and Gerda C
 laeskens.\n\nhttp://www.uni-goettingen.de/de/101995.html
LOCATION:MR12\, CMS\, Wilberforce Road\, Cambridge\, CB3 0WB
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