arXiv subjects

Serguey Pergamenshchikov

Publications and source records attributed to Serguey Pergamenshchikov.

4 recordsLinked to original sources

arXiv2008

Adaptive asymptotically efficient estimation in heteroscedastic nonparametric regression via model selection

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.

math.ST↗

arXiv2008

Adaptive nonparametric estimation in heteroscedastic regression models. Part 2: Asymptotic efficiency

The paper deals with asymptotic properties of the adaptive procedure proposed in the author paper (2007) for estimation of unknown nonparametric regression. We prove that this procedure is asymptotically efficient for a quadratic risk. It means that the asymptotic quadratic risk for this procedure coincides with a sharp lower bound.

math.ST↗

arXiv2008

Adaptive sequential estimation for ergodic diffusion processes in quadratic metric. Part 2: Asymptotic efficiency

Asymptotic efficiency is proved for the constructed in part 1 procedure, i.e. Pinsker's constant is found in the asymptotic lower bound for the minimax quadratic risk. It is shown that the asymptotic minimax quadratic risk of the constructed procedure coincides with this constant.

math.ST↗

arXiv2008

Adaptive nonparametric estimation in heteroscedastic regression models. Part 1: Sharp non-asymptotic Oracle inequalities

An adaptive nonparametric estimation procedure is constructed for the estimation problem of heteroscedastic regression when the noise variance depends on the unknown regression. A non-asymptotic upper bound for a quadratic risk (an oracle inequality) is constructed.

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