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SUMMARY:Uniform limit theorems for wavelet density estimators - Evarist Gi
 ne (University of Conneticut)
DTSTART:20081020T130000Z
DTEND:20081020T143000Z
UID:TALK14319@talks.cam.ac.uk
CONTACT:10918
DESCRIPTION:The linear wavelet density estimator of a bounded density f co
 nsists of a truncated wavelet\nexpansion with the coefficients for the exp
 ansion of f replaced by their empirical counterparts. The\noptimal number 
 of terms of the expansion\, obtained by balancing bias and variance\, depe
 nds on the\ndegree of smoothness of f\, typically unknown. Donoho-Johnston
 e-Kerkyacharian-Picard (1996)\nintroduced the `hard thresholding' wavelet 
 density estimator  -where part of the empirical\ncoefficients are set equ
 al to zero if they are smaller than a certain threshold- in order to obtai
 n\nan estimator which is rate adaptive in L_p norm loss to the smoothness 
 of f\, up to a logarithmic\nfactor. The sup-norm behavior of wavelet densi
 ty estimators (thresholded or not) had not been\nconsidered before\, and w
 e use empirical process theory to close this gap\, thus deriving optimal\n
 results first for the linear and then for the thresholded estimator. This 
 is joint work with Richard\nNickl.\n
LOCATION:MR12\, CMS\, Wilberforce Road\, Cambridge\, CB3 0WB
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