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SUMMARY:On adaptive nonparametric inference - Richard Nickl (Cambridge)
DTSTART:20101119T160000Z
DTEND:20101119T170000Z
UID:TALK25763@talks.cam.ac.uk
CONTACT:Richard Nickl
DESCRIPTION:\nOne of the intriguing problems in the paradigm of adaptive\n
 nonparametric function estimation as developed in the last two decades by\
 nDonoho\, Johnstone\, Lepski\, Birge\, Massart\, Kerkyacharian\, Picard\, 
 Tsybakov\,\nSpokoiny\, Cai\, Low and many others\, is what one could call 
 the 'hiatus'\nbetween estimation and inference\, or\, to be more precise\,
  between the\nexistence of adaptive risk bounds and the non-existence of a
 daptive\nconfidence statements. Considering the fundamental problem of the
  existence\nof adaptive confidence bands\, we show that this fact is deepl
 y connected to\ncertain nonparametric hypothesis testing problems studied 
 by the Russian\nschool (Ingster and others)\, and we use this connection t
 o derive necessary\nand sufficient conditions for the existence of adaptiv
 e confidence\nstatements\, thus characterising the exact boundaries of whe
 n adaptive\ninference is possible and when not.\n
LOCATION:MR12\, CMS\, Wilberforce Road\, Cambridge\, CB3 0WB
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