Adaptive de-noising of signals satisfying differential inequalities

Alexander Goldenshluger; Arkadi Nemirovski

doi:10.1109/18.568698

Adaptive de-noising of signals satisfying differential inequalities

Alexander Goldenshluger, Arkadi Nemirovski

Research output: Contribution to journal › Article › peer-review

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 measures.

Original language	English
Pages (from-to)	872-889
Number of pages	18
Journal	IEEE Transactions on Information Theory
Volume	43
Issue number	3
DOIs	https://doi.org/10.1109/18.568698
State	Published - 1997
Externally published	Yes

Keywords

Adaptation
Differential inequalities
Lower bounds
Minimax risk
Nonparametric estimation
Optimal in order estimators

ASJC Scopus subject areas

Information Systems
Computer Science Applications
Library and Information Sciences

Access to Document

10.1109/18.568698

Cite this

@article{d5109fcaf8574abd9aa48bde5469bfeb,

title = "Adaptive de-noising of signals satisfying differential inequalities",

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 measures.",

keywords = "Adaptation, Differential inequalities, Lower bounds, Minimax risk, Nonparametric estimation, Optimal in order estimators",

author = "Alexander Goldenshluger and Arkadi Nemirovski",

year = "1997",

doi = "10.1109/18.568698",

language = "English",

volume = "43",

pages = "872--889",

journal = "IEEE Transactions on Information Theory",

issn = "0018-9448",

publisher = "Institute of Electrical and Electronics Engineers Inc.",

number = "3",

}

TY - JOUR

T1 - Adaptive de-noising of signals satisfying differential inequalities

AU - Goldenshluger, Alexander

AU - Nemirovski, Arkadi

PY - 1997

Y1 - 1997

N2 - 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.

AB - 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.

KW - Adaptation

KW - Differential inequalities

KW - Lower bounds

KW - Minimax risk

KW - Nonparametric estimation

KW - Optimal in order estimators

UR - http://www.scopus.com/inward/record.url?scp=0031139385&partnerID=8YFLogxK

U2 - 10.1109/18.568698

DO - 10.1109/18.568698

M3 - Article

AN - SCOPUS:0031139385

SN - 0018-9448

VL - 43

SP - 872

EP - 889

JO - IEEE Transactions on Information Theory

JF - IEEE Transactions on Information Theory

IS - 3

ER -

Adaptive de-noising of signals satisfying differential inequalities

Abstract

Keywords

ASJC Scopus subject areas

Access to Document

Other files and links

Fingerprint

Cite this