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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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.


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.

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

First available in Project Euclid: 24 September 2008

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Zentralblatt MATH identifier

Primary: 62G05: Estimation 62G20: Asymptotic properties

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


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.

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