9 citations · 25 across the 10 of their papers we have counts for
4 papers · 1 filter
On some estimates for bounded submartingales and the shift inequality
Leonid Galtchouk, Isaac Sonin
It is well known that if a submartingale is bounded then the increasing predictable process and the martingale from the Doob decomposition can be unbounded. I…
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 asymptotically efficient estimation in heteroscedastic nonparametric regression
Leonid Galtchouk, Serguei Pergamenchtchikov
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…
Geometric ergodicity for families of homogeneous Markov chains
Leonid Galtchouk, Serguei Pergamenchtchikov
In this paper we find nonasymptotic exponential upper bounds for the deviation in the ergodic theorem for families of homogeneous Markov processes. We find some sufficient conditio…