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Adaptive de-noising of signals satisfying differential inequalities

机译:满足差分不等式的信号的自适应去噪

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摘要

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 an estimator which is optimal in order over a wide range of the classes and "discrete" global accuracy measures.
机译:本文致力于通过给定阶数的未知微分算子满足线性微分不等式的信号的空间自适应估计。所考虑的信号类别涵盖非参数回归常见的多种类别。特别地,它们包含其平滑度参数不是均匀有界的信号,甚至局部信号也没有。我们开发了一种估算器,该估算器在各种类别和“离散”全局精度测度中顺序最佳。

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