Adaptive asymptotically efficient estimation in heteroscedastic nonparametric regression via model selection

Details Adaptive asymptotically efficient estimation in heteroscedastic nonparametric regression via model selection Adaptive asymptotically efficient estimation in heteroscedastic nonparametric regression via model selection

2008-10-07

arxiv.org/abs/0810.1173v1

Mathematics

Statistics Theory

Scientific paper

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 estimators.

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