Change-point estimation from indirect observations. 2. Adaptation
Annales de l'I.H.P. Probabilités et statistiques, Tome 44 (2008) no. 5, pp. 819-836.

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.

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.

DOI : 10.1214/07-AIHP144
Classification : 62G05, 62G20
Mots-clés : singularities, change-point, estimation, detection, minimax risk, adaption, optimal rates 
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Goldenshluger, A.; Juditsky, A.; Tsybakov, A.; Zeevi, A. Change-point estimation from indirect observations. 2. Adaptation. Annales de l'I.H.P. Probabilités et statistiques, Tome 44 (2008) no. 5, pp. 819-836. doi : 10.1214/07-AIHP144. http://archive.numdam.org/articles/10.1214/07-AIHP144/

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