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

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

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.

Original language	English
Pages (from-to)	787-818
Number of pages	32
Journal	Annales de l'institut Henri Poincare (B) Probability and Statistics
Volume	44
Issue number	5
DOIs	https://doi.org/10.1214/07-AIHP110
Publication status	Published - 1 Oct 2008

Keywords

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

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10.1214/07-AIHP110

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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",

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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

UR - https://www.scopus.com/pages/publications/77951843654

U2 - 10.1214/07-AIHP110

DO - 10.1214/07-AIHP110

M3 - Article

AN - SCOPUS:77951843654

SN - 0246-0203

VL - 44

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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

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