Change-point estimation from indirect observations. 1. Minimax complexity

A. Goldenshluger; A. Juditsky; A. B. Tsybakov; A. Zeevi

doi:10.1214/07-AIHP110

Change-point estimation from indirect observations. 1. Minimax complexity

A. Goldenshluger
, A. Juditsky
, A. B. Tsybakov
, A. Zeevi

University of Haifa
LMC-IMAG
Columbia University

Résultats de recherche: Contribution à un journal › Article › Revue par des pairs

Résumé

We consider the problem of nonparametric estimation of signal singularities from indirect and noisy observations. Here by singularity, we mean a discontinuity (change-point) of the signal or of its derivative. The model of indirect observations we consider is that of a linear transform of the signal, observed in white noise. The estimation problem is analyzed in a minimax framework. We provide lower bounds for minimax risks and propose rate-optimal estimation procedures.

langue originale	Anglais
Pages (de - à)	787-818
Nombre de pages	32
journal	Annales de l'institut Henri Poincare (B) Probability and Statistics
Volume	44
Numéro de publication	5
Les DOIs	https://doi.org/10.1214/07-AIHP110
état	Publié - 1 oct. 2008

Accès au document

10.1214/07-AIHP110

Contient cette citation

@article{557200b226364342a2c0708fe5e09130,

title = "Change-point estimation from indirect observations. 1. Minimax complexity",

abstract = "We consider the problem of nonparametric estimation of signal singularities from indirect and noisy observations. Here by singularity, we mean a discontinuity (change-point) of the signal or of its derivative. The model of indirect observations we consider is that of a linear transform of the signal, observed in white noise. The estimation problem is analyzed in a minimax framework. We provide lower bounds for minimax risks and propose rate-optimal estimation procedures.",

keywords = "Change-point estimations, Ill-posed problems, Minimax risk, Optimal rates of convergence, Sequence space model",

author = "A. Goldenshluger and A. Juditsky and Tsybakov, \{A. B.\} and A. Zeevi",

year = "2008",

month = oct,

day = "1",

doi = "10.1214/07-AIHP110",

language = "English",

volume = "44",

pages = "787--818",

journal = "Annales de l'institut Henri Poincare (B) Probability and Statistics",

issn = "0246-0203",

number = "5",

}

TY - JOUR

T1 - Change-point estimation from indirect observations. 1. Minimax complexity

AU - Goldenshluger, A.

AU - Juditsky, A.

AU - Tsybakov, A. B.

AU - Zeevi, A.

PY - 2008/10/1

Y1 - 2008/10/1

N2 - We consider the problem of nonparametric estimation of signal singularities from indirect and noisy observations. Here by singularity, we mean a discontinuity (change-point) of the signal or of its derivative. The model of indirect observations we consider is that of a linear transform of the signal, observed in white noise. The estimation problem is analyzed in a minimax framework. We provide lower bounds for minimax risks and propose rate-optimal estimation procedures.

AB - We consider the problem of nonparametric estimation of signal singularities from indirect and noisy observations. Here by singularity, we mean a discontinuity (change-point) of the signal or of its derivative. The model of indirect observations we consider is that of a linear transform of the signal, observed in white noise. The estimation problem is analyzed in a minimax framework. We provide lower bounds for minimax risks and propose rate-optimal estimation procedures.

KW - Change-point estimations

KW - Ill-posed problems

KW - Minimax risk

KW - Optimal rates of convergence

KW - Sequence space model

U2 - 10.1214/07-AIHP110

DO - 10.1214/07-AIHP110

M3 - Article

AN - SCOPUS:77951843654

SN - 0246-0203

VL - 44

SP - 787

EP - 818

JO - Annales de l'institut Henri Poincare (B) Probability and Statistics

JF - Annales de l'institut Henri Poincare (B) Probability and Statistics

IS - 5

ER -

Change-point estimation from indirect observations. 1. Minimax complexity

Résumé

Accès au document

Empreinte digitale

Contient cette citation