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SUMMARY:Simultaneous local and global adaptivity of Bayesian wavelet  esti
 mators in nonparametric regression - Natalia Bochkina (Edinburgh)
DTSTART:20110128T160000Z
DTEND:20110128T170000Z
UID:TALK28561@talks.cam.ac.uk
CONTACT:Richard Nickl
DESCRIPTION:We consider Bayesian wavelet estimators in the context of\nnon
 parametric regression. The most commonly used wavelet\nestimators are sepa
 rable\, i.e. estimator of\neach wavelet coefficient is based only on its o
 wn observation.\nHowever\, as it was shown by Cai (2008) for the white noi
 se model\,\nadaptive separable estimators cannot achieve\n  minimax-optima
 l  rate in L_2 norm (global rate) without paying the  price\nfor adaptivit
 y.\nThe nonseparable estimator of Johnstone and Silverman\n(2005) that use
 s maximum marginal likelihood approach to estimate\nsome of the parameters
 \, and achieves the optimal global rate\, in\nfact can be interpreted as a
  Bayesian estimator. We show that it\nalso achieves adaptive minimax-optim
 al local rate\,\nand discuss other Bayesian wavelet estimators that pool i
 nformation\ntogether across wavelet coefficients.\n\nBayesian wavelet mode
 lling is usually done in the domain of\nwavelet coefficients. We discuss h
 ow a priori assumptions in\nwavelet domain transfer to the function domain
  for the considered\nestimators.\nPart of this work is joint with T.Sapati
 nas (University of Cyprus).\n\n\n\nhttp://www.maths.ed.ac.uk/people/show/p
 erson/101
LOCATION:MR12\, CMS\, Wilberforce Road\, Cambridge\, CB3 0WB
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