Some new ideas in nonparametric estimation
Statistics Theory
2016-03-15 v1 Statistics Theory
Abstract
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 and establishing for the selected estimator so-called oracle inequality. %parameterized by some se t. If is the selected parameter and is an estimator's collection built in {\it Problem B} we suggest to use the estimator . We present very general selection rule led to selector and find conditions under which the estimator is reasonable. Our approach is illustrated by several examples related to adaptive estimation.
Cite
@article{arxiv.1603.03934,
title = {Some new ideas in nonparametric estimation},
author = {Oleg Lepski},
journal= {arXiv preprint arXiv:1603.03934},
year = {2016}
}