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Author Cavalier, Laurent ♦ Tsybakov, Alexandre
Source SpringerLink
Content type Text
Publisher Springer-Verlag
File Format PDF
Copyright Year ©2002
Language English
Subject Domain (in DDC) Social sciences ♦ Sociology & anthropology
Abstract  We consider a heteroscedastic sequence space setup with polynomially increasing variances of observations that allows to treat a number of inverse problems, in particular multivariate ones. We propose an adaptive estimator that attains simultaneously exact asymptotic minimax constants on every ellipsoid of functions within a wide scale (that includes ellipoids with polynomially and exponentially decreasing axes) and, at the same time, satisfies asymptotically exact oracle inequalities within any class of linear estimates having monotone non-increasing weights. The construction of the estimator is based on a properly penalized blockwise Stein's rule, with weakly geometically increasing blocks. As an application, we construct sharp adaptive estimators in the problems of deconvolution and tomography.
ISSN 01788051
Age Range 18 to 22 years ♦ above 22 year
Educational Use Research
Education Level UG and PG
Learning Resource Type Article
Publisher Date 2002-07-01
Publisher Place Berlin/Heidelberg
e-ISSN 14322064
Journal Probability Theory and Related Fields
Volume Number 123
Issue Number 3
Page Count 32
Starting Page 323
Ending Page 354

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Source: SpringerLink