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.

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Authors
Alexander Goldenshluger, A. Juditsky, A. Tsybakov, and Assaf Zeevi
Format
Journal Article
Publication Date
Journal
Annales de l'Institut Henri Poincaré, Probabilités et Statistiques

Full Citation

Goldenshluger, Alexander, A. Juditsky, A. Tsybakov, and Assaf Zeevi
. “Change-point estimation from indirect observations. 2. Adaptation.”
Annales de l'Institut Henri Poincaré, Probabilités et Statistiques
vol.
44
, (January 01, 2008):
819
-
836
.