Change-point estimation from indirect observations. 2. Adaptation
A. Goldenshluger, A. Juditsky, A. Tsybakov and A. Zeevi
Ann. Inst. H. Poincare Probab. Statist. Volume 44, Number 5, pp. 819-836, 2008.

Abstract

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

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