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CATEGORIES:Statistics
SUMMARY:Information bounds for inverse problems with appli
cation to deconvolution and Lévy models - Mathias
Trabs (CEREMADE\, Paris Dauphine)
DTSTART;TZID=Europe/London:20160304T160000
DTEND;TZID=Europe/London:20160304T170000
UID:TALK64780AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/64780
DESCRIPTION:If a functional in a nonparametric inverse problem
can be estimated with parametric rate\, then the
minimax rate gives no information about the ill-po
sedness of the problem. To have a more precise low
er bound\, we study semiparametric efficiency in t
he sense of Hájek–Le Cam for functional estimation
in regular indirect models. These are characteriz
ed as models that can be locally approximated by a
linear white noise model that is described by the
generalized score operator. A convolution theorem
for regular indirect models is proved. This appli
es to a large class of statistical inverse problem
s\, which is illustrated for the prototypical whit
e noise and deconvolution model. It is especially
useful for nonlinear models. We discuss in detail
a nonlinear model of deconvolution type where a Lé
vy process is observed at low frequency\, concludi
ng an information bound for the estimation of line
ar functionals of the jump measure.
LOCATION:MR12\, Centre for Mathematical Sciences\, Wilberfo
rce Road\, Cambridge.
CONTACT:Quentin Berthet
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