7 citations · 12 across the 5 of their papers we have counts for
5 papers
Efficient pointwise estimation based on discrete data in ergodic nonparametric diffusions
L. I. Galtchouk, S. M. Pergamenshchikov
A truncated sequential procedure is constructed for estimating the drift coefficient at a given state point based on discrete data of ergodic diffusion process. A nonasymptotic upp…
Sharp non-asymptotic oracle inequalities for nonparametric heteroscedastic regression models
Leonid Galtchouk, Serguei Pergamenchtchikov
An adaptive nonparametric estimation procedure is constructed for heteroscedastic regression when the noise variance depends on the unknown regression. A non-asymptotic upper bound…
Adaptive nonparametric estimation in heteroscedastic regression models. Part 1: Sharp non-asymptotic Oracle inequalities
Leonid Galtchouk, Serguey Pergamenshchikov
An adaptive nonparametric estimation procedure is constructed for the estimation problem of heteroscedastic regression when the noise variance depends on the unknown regression. A…
Adaptive sequential estimation for ergodic diffusion processes in quadratic metric. Part 2: Asymptotic efficiency
Leonid Galtchouk, Serguey Pergamenshchikov
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…
Adaptive nonparametric estimation in heteroscedastic regression models. Part 2: Asymptotic efficiency
Leonid Galtchouk, Serguey Pergamenshchikov
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 proc…