Adaptive asymptotically efficient estimation in heteroscedastic nonparametric regression

The paper considers some asymptotic properties of the adaptive procedure proposed in authors' paper, 2007, for estimating an unknown nonparametric regression. We show that the procedure is asymptotically efficient for quadratic risk, i.e. the asymptotic quadratic risk of the procedure coincides with the corresponding Pinsker constant provided the sharp lower bound for the quadratic risk over all possible estimators.