Adaptive de-noising of signals satisfying differential inequalities
- 1 May 1997
- journal article
- Published by Institute of Electrical and Electronics Engineers (IEEE) in IEEE Transactions on Information Theory
- Vol. 43 (3) , 872-889
- https://doi.org/10.1109/18.568698
Abstract
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 measuresKeywords
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