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SUMMARY:Information bounds for inverse problems with application to deconv
 olution and Lévy models - Mathias Trabs (CEREMADE\, Paris Dauphine)
DTSTART:20160304T160000Z
DTEND:20160304T170000Z
UID:TALK64780@talks.cam.ac.uk
CONTACT:Quentin Berthet
DESCRIPTION:If a functional in a nonparametric inverse problem can be esti
 mated with parametric rate\, then the minimax rate gives no information ab
 out the ill-posedness of the problem. To have a more precise lower bound\,
  we study semiparametric efficiency in the sense of Hájek–Le Cam for fu
 nctional estimation in regular indirect models. These are characterized as
  models that can be locally approximated by a linear white noise model tha
 t is described by the generalized score operator. A convolution theorem fo
 r regular indirect models is proved. This applies to a large class of stat
 istical inverse problems\, which is illustrated for the prototypical white
  noise and deconvolution model. It is especially useful for nonlinear mode
 ls. We discuss in detail a nonlinear model of deconvolution type where a L
 évy process is observed at low frequency\, concluding an information boun
 d for the estimation of linear functionals of the jump measure.
LOCATION:MR12\, Centre for Mathematical Sciences\, Wilberforce Road\, Camb
 ridge.
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