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The paper deals with asymptotic properties of the adaptive procedure proposedin the author paper, 2007, for estimating a unknown nonparametric regression.We prove that this procedure is asymptotically efficient for a quadratic risk,i.e. the asymptotic quadratic risk for this procedure coincides with thePinsker constant which gives a sharp lower bound for the quadratic risk overall possible estimators.

Adaptive asymptotically efficient estimation in heteroscedastic nonparametric regression via model selection