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