Some new ideas in nonparametric estimation

In the framework of an abstract statistical model we discuss how to use the solution of one estimation problem ({\it Problem A}) in order to construct an estimator in another, completely different, {\it Problem B}. As a solution of {\it Problem A} we understand a data-driven selection from a given family of estimators $\mathbf{A}(\text{mH})=\{{\widehat{A}}_{\text{mh}},\text{mh}\in \text{mH}\}$ and establishing for the selected estimator so-called oracle inequality. %parameterized by some se t$\text{mH}$. If $\widehat{\text{mh}}\in \text{mH}$ is the selected parameter and $\mathbf{B}(\text{mH})=\{{\widehat{B}}_{\text{mh}},\text{mh}\in \text{mH}\}$ is an estimator’s collection built in {\it Problem B} we suggest to use the estimator ${\widehat{B}}_{\widehat{\text{mh}}}$. We present very general selection rule led to selector $\widehat{\text{mh}}$ and find conditions under which the estimator ${\widehat{B}}_{\widehat{\text{mh}}}$ is reasonable. Our approach is illustrated by several examples related to adaptive estimation.