Adaptive asymptotically efficient estimation in heteroscedastic nonparametric regression

@inproceedings{Galtchouk2008AdaptiveAE,
  title={Adaptive asymptotically efficient estimation in heteroscedastic nonparametric regression},
  author={Leonid Galtchouk and Sergey Pergamenshchikov},
  year={2008}
}
The paper deals with asymptotic properties of the adaptive procedure proposed in 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 the Pinsker constant which gives a sharp lower bound for the quadratic risk over all possible estimates. 1 2 1 AMS 2000 Subject Classification : primary 62G08; secondary 62G05, 62G20 2 

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