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CATEGORIES:Statistics
SUMMARY:Uniform limit theorems for wavelet density estimat
ors - Evarist Gine (University of Conneticut)
DTSTART;TZID=Europe/London:20081020T140000
DTEND;TZID=Europe/London:20081020T153000
UID:TALK14319AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/14319
DESCRIPTION:The linear wavelet density estimator of a bounded
density f consists of a truncated wavelet\nexpansi
on with the coefficients for the expansion of f re
placed by their empirical counterparts. The\noptim
al number of terms of the expansion\, obtained by
balancing bias and variance\, depends on the\ndegr
ee of smoothness of f\, typically unknown. Donoho-
Johnstone-Kerkyacharian-Picard (1996)\nintroduced
the `hard thresholding' wavelet density estimator
-where part of the empirical\ncoefficients are se
t equal to zero if they are smaller than a certain
threshold- in order to obtain\nan estimator which
is rate adaptive in L_p norm loss to the smoothne
ss of f\, up to a logarithmic\nfactor. The sup-nor
m behavior of wavelet density estimators (threshol
ded or not) had not been\nconsidered before\, and
we use empirical process theory to close this gap\
, thus deriving optimal\nresults first for the lin
ear and then for the thresholded estimator. This i
s joint work with Richard\nNickl.\n
LOCATION:MR12\, CMS\, Wilberforce Road\, Cambridge\, CB3 0W
B
CONTACT:
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