  The paper deals with asymptotic properties of the adaptive procedure proposed
in the author paper, 2007, for estimating an unknown nonparametric regression.
%\cite{GaPe1}. We prove that this procedure is asymptotically efficient for a
quadratic risk, i.e. the asymptotic quadratic risk for this procedure coincides
with the Pinsker constant which gives a sharp lower bound for the quadratic
risk over all possible estimates
