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SUMMARY:The 1995 wavelet paper of Donoho\, Johnstone\, Kerkyacharian and P
 icard - Richard Nickl\, University of Cambridge
DTSTART:20081126T163000Z
DTEND:20081126T173000Z
UID:TALK14655@talks.cam.ac.uk
CONTACT:Richard Samworth
DESCRIPTION:The minimax paradigm in statistical function estimation is a q
 uite flexible\nbut also complicated way to assess the performance of stati
 stical estimation\nprocedures in cases where the parameter space is infini
 te-dimensional. It\nusually consists of\n\na) an observational model\, e.g
 .\, regression\, density\, white noise\, etc.\; \nb) a prescribed infinite
 -dimensional parameter space over which one wants to\nhave a uniformly opt
 imal procedure\;\nc) a loss function on the parameter space that measures 
 closeness and hence\n'optimality'\n\nIn discussing the paper\, we will fir
 st see that all permutations of possible\nchoices in a)-c) lead to a quite
  confusing (but not meaningless) complexity\,\nwhich basically poses two m
 ain statistical challenges: 'Spatial Adaptation'\nand 'Adaptation to unkno
 wn smoothness'.\n\nThe main discussion of the paper will then focus on the
  remarkable fact that\nthe authors provided a universal\, simple and compu
 table 'nearly optimal'\nsimultaneous solution to all these problems by mea
 ns of a 'wavelet shrinkage' estimation procedure\, that I will try to expl
 ain in some detail\,\nincluding a quick crash course in wavelets.\n\nThe l
 ink to the paper\, with discussion\, is here\n\nhttp://www.jstor.org/stabl
 e/pdfplus/2345967.pdf\n\n
LOCATION:MR11\, CMS
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