Annales de l'Institut Henri Poincaré, Probabilités et Statistiques

Change-point estimation from indirect observations. 2. Adaptation

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

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Abstract

We focus on the problem of adaptive estimation of signal singularities from indirect and noisy observations. A typical example of such a singularity is a discontinuity (change-point) of the signal or of its derivative. We develop a change-point estimator which adapts to the unknown smoothness of a nuisance deterministic component and to an unknown jump amplitude. We show that the proposed estimator attains optimal adaptive rates of convergence. A simulation study demonstrates reasonable practical behavior of the proposed adaptive estimates.

Résumé

Nous étudions ici le problème d’estimation adaptative de singularités d’un signal à partir des observations indirectes et bruitées. Par exemple, cette definition de singularité inclut des points de discontinuité (points de rupture) du signal ou de ses derivées. Nous proposons un estimateur du point de rupture qui s’adapte à une regularité inconnue du paramètre de nuisance et à l’amplitude inconnue du saut, et dont la vitesse de convergence est optimale. Nous illustrons les propriétés théoriques de cet estimateur par quelques résultats de simulation.

Article information

Source
Ann. Inst. H. Poincaré Probab. Statist., Volume 44, Number 5 (2008), 819-836.

Dates
First available in Project Euclid: 24 September 2008

Permanent link to this document
https://projecteuclid.org/euclid.aihp/1222261914

Digital Object Identifier
doi:10.1214/07-AIHP144

Mathematical Reviews number (MathSciNet)
MR2453846

Zentralblatt MATH identifier
1206.62047

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

Keywords
Singularities Change-point Estimation Detection Minimax risk Adaption Optimal rates

Citation

Goldenshluger, A.; Juditsky, A.; Tsybakov, A.; Zeevi, A. Change-point estimation from indirect observations. 2. Adaptation. Ann. Inst. H. Poincaré Probab. Statist. 44 (2008), no. 5, 819--836. doi:10.1214/07-AIHP144. https://projecteuclid.org/euclid.aihp/1222261914


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References

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