On Spatial Adaptive Nonparametric Estimation of Functions Satisfying Differential Inequalities
نویسنده
چکیده
The paper is devoted to developing spatial adaptive estimates of the signals satisfying linear differential inequalities with unknown differential operator of a given order. The classes of signals under consideration cover a wide variety of classes usual in the nonparametric regression problem; moreover, they contain the signals whose parameters of smoothness are not uniformly bounded, even locally. We develop the estimate which is optimal in order over these classes and wide range of “discrete” global accuracy measures.
منابع مشابه
Adaptive de-noising of signals satisfying differential inequalities
The paper is devoted to spatial adaptive estimation of signals satisfying linear differential inequalities with an unknown differential operator of a given order. The classes of signals under consideration cover a wide variety of classes common to nonparametric regression. In particular, they contain the signals whose parameters of smoothness are not uniformly bounded, even locally. We develop ...
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