Change-point estimation from indirect observations. 2. Adaptation
A. Goldenshluger, A. Juditsky, A. Tsybakov, A. Zeevi (2008)
Annales de l'I.H.P. Probabilités et statistiques
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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...