Annales de l'Institut Henri Poincaré, Probabilités et Statistiques

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

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

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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.

Résumé

Cet article a pour but d’étudier le problème d’estimation non-paramétrique de singularités d’un signal à partir des observations indirectes et bruitées. Les singularités que nous considérons ici sont des points de discontinuité (points de rupture) du signal ou de ses derivées. Nous étudions le modèle où l’on dispose d’observations indirectes d’une transformée linéaire du signal dans le bruit blanc gaussien. Le problème de l’estimation est analysé dans un cadre minimax. Nous obtenons des minorations du risque minimax et nous proposons des estimateurs qui sont optimaux en vitesse de convergence.

Article information

Source
Ann. Inst. H. Poincaré Probab. Statist., Volume 44, Number 5 (2008), 787-818.

Dates
First available in Project Euclid: 24 September 2008

Permanent link to this document
https://projecteuclid.org/euclid.aihp/1222261913

Digital Object Identifier
doi:10.1214/07-AIHP110

Mathematical Reviews number (MathSciNet)
MR2453845

Zentralblatt MATH identifier
1206.62048

Subjects
Primary: 62G05: Estimation 62G20: Asymptotic properties

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

Citation

Goldenshluger, A.; Juditsky, A.; Tsybakov, A. B.; Zeevi, A. Change-point estimation from indirect observations. 1. Minimax complexity. Ann. Inst. H. Poincaré Probab. Statist. 44 (2008), no. 5, 787--818. doi:10.1214/07-AIHP110. https://projecteuclid.org/euclid.aihp/1222261913


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